Phase-protecting reagent flow orderings for use in sequencing-by-synthesis

ABSTRACT

A method for nucleic acid sequencing includes: disposing a plurality of template polynucleotide strands, sequencing primers, and polymerases in a plurality of defined spaces of a sensor array; exposing template polynucleotide strands to a series of flows of nucleotide species, the series comprising a sequence of random flows; and obtaining, for each of the series of flows of nucleotide species, a signal indicative of how many nucleotide incorporations occurred for that particular flow to determine a predicted sequence of nucleotides corresponding to the template polynucleotide strands.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/440,849, filed Apr. 5, 2012, which claims the benefit of U.S. Prov.Pat. Appl. No. 61/473,721 filed Apr. 8, 2011, U.S. Prov. Pat. Appl. No.61/544,924 filed Oct. 7, 2011, U.S. Prov. Pat. Appl. No. 61/549,407filed Oct. 20, 2011, and U.S. Prov. Pat. Appl. No. 61/617,231 filed Mar.29, 2012, which are all incorporated by reference herein in theirentirety.

SEQUENCE LISTING

This application contains a Sequence Listing, which has been submittedin ASCII format via EFS-Web in parent application U.S. patentapplication Ser. No. 13/440,849 and is hereby incorporated by referencein its entirety. Said ASCII copy is named LT00490_ST25.txt, was createdon Jun. 22, 2012, and is 5,334 bytes in size.

FIELD

This application generally relates to methods, systems, apparatuses, andcomputer readable media for nucleic acid sequencing, and, morespecifically, to methods, systems, apparatuses, and computer readablemedia involving various phase-protecting reagent flow orderings for usein sequencing-by-synthesis.

BACKGROUND

Various instruments, apparatuses, and/or systems for sequencing nucleicacids sequence nucleic acids using sequencing-by-synthesis. Suchinstruments, apparatuses, and/or systems may include, for example, theGenome Analyzer/HiSeq/MiSeq platforms (Illumina, Inc.; see, e.g., U.S.Pat. Nos. 6,833,246 and 5,750,341); the GS FLX, GS FLX Titanium, and GSJunior platforms (Roche/454 Life Sciences; see, e.g., Ronaghi et al.,SCIENCE, 281:363-365 (1998), and Margulies et al., NATURE, 437:376-380(2005)); and the Ion Personal Genome Machine (PGM™) and Ion Proton™(Life Technologies Corp./Ion Torrent; see, e.g., U.S. Pat. No. 7,948,015and U.S. Pat. Appl. Publ. Nos. 2010/0137143, 2009/0026082, and2010/0282617, which are all incorporated by reference herein in theirentirety). In order to increase sequencing efficiency and/or accuracy,there is a need for new methods, systems, apparatuses, and computerreadable media that perform sequencing-by-synthesis while reducing orminimizing sequencing errors associated with various phase loss effectsthat may occur with sequencing-by-synthesis.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated into and form a partof the specification, illustrate one or more exemplary embodiments andserve to explain the principles of various exemplary embodiments. Thedrawings are exemplary and explanatory only and are not to be construedas limiting or restrictive in any way.

FIG. 1 illustrates components of an exemplary system for nucleic acidsequencing.

FIG. 2A illustrates cross-sectional and expanded views of an exemplaryflow cell for nucleic acid sequencing.

FIG. 2B illustrates an exemplary uniform flow front between successivereagents moving across a section of an exemplary microwell array.

FIG. 3A illustrates exemplary flow paths through an exemplary flowchamber having diagonally opposed inlet and outlet.

FIG. 3B illustrates an exemplary flow chamber with an exemplary sensorarray area defined by reference to a reach of reagent flow paths.

FIGS. 4A and 4B illustrate schematically an exemplary process forlabel-free, pH-based sequencing.

FIGS. 4C-4P illustrate schematically exemplary flow-based steps forsequencing a target using sequencing-by-synthesis.

FIG. 4Q illustrates exemplary raw pH-based sequencing data correspondingto counts associated with a plurality of nucleotide flows.

FIG. 4R illustrates exemplary flow-by-flow numerical valuescorresponding to raw pH-based sequencing data from which homopolymerlength predictions can be made.

FIG. 5 illustrates exemplary incomplete extension (IE) and carry forward(CF) events that may occur and result in loss of phasic synchrony duringsequencing-by-synthesis. FIG. 5 discloses SEQ ID NO: 1.

FIG. 6A illustrates an exemplary system for obtaining, processing,and/or analyzing nucleic acid sequencing data.

FIG. 6B illustrates an exemplary method for obtaining, processing,and/or analyzing nucleic acid sequencing data.

FIG. 7A illustrates exemplary simulation data corresponding to signalresponse curves for an exemplary cyclical, repeating flow ordering of“GATC GATC . . . .”

FIG. 7B illustrates exemplary simulation data corresponding to templatepopulation evolution as sequencing progresses for the cyclical,repeating flow ordering of FIG. 7A.

FIG. 8A illustrates exemplary simulation data corresponding to signalresponse curves for an exemplary flow ordering of “TACG TACG TACG TACGTACG TACAT ACGCA CGTGC GTATG” (SEQ ID NO: 2).

FIG. 8B illustrates exemplary simulation data corresponding to templatepopulation evolution as sequencing progresses for the flow ordering ofFIG. 8A.

FIG. 9A illustrates exemplary simulation data corresponding to signalresponse curves for an exemplary flow ordering of “TACG TACG TCTG AGCA”(SEQ ID NO: 3).

FIG. 9B illustrates exemplary simulation data corresponding to templatepopulation evolution as sequencing progresses for the flow ordering ofFIG. 9A.

FIG. 10A illustrates an exemplary adjacency matrix representation for anexemplary cyclical, repeating flow ordering of “TACG TACG . . . .”

FIG. 10B illustrates an exemplary adjacency matrix representation forthe flow ordering of FIG. 9A.

FIG. 10C illustrates an exemplary adjacency matrix representation forthe flow ordering of FIG. 8A.

FIG. 11 illustrates an exemplary graph showing trade-offs betweenefficiency of extension and dephasing merit for eight exemplary floworderings.

FIG. 12A illustrates exemplary simulation data corresponding to signalresponse curves for an exemplary cyclical, repeating flow ordering of“TACG TACG . . . .”

FIG. 12B illustrates exemplary simulation data corresponding to templatepopulation evolution as sequencing progresses for the cyclical,repeating flow ordering of FIG. 12A.

FIG. 13A illustrates exemplary simulation data corresponding to signalresponse curves for an exemplary flow ordering of “TACG TACG TAGC TTGACGTA CGTC ATGC ATCG ATCA GCTA AGCT GACG TAGC TAGC ATCG ATCC AGTC ATGACTGA CGTA GCTG ACTG GATC AGTC ATGC ATCG” (SEQ ID NO: 4).

FIG. 13B illustrates exemplary simulation data corresponding to templatepopulation evolution as sequencing progresses for the flow ordering ofFIG. 13A.

FIG. 14A illustrates exemplary simulation data corresponding to signalresponse curves for an exemplary flow ordering of “TACG TACG TAGC TGACGTAC GTCA TGCA TCGA TCAG CTAG CTGA CGTA GCTA GCAT CGAT CAGT CATG ACTGACGT AGCT GACT GATC AGTC ATGC ATCG” (SEQ ID NO: 5).

FIG. 14B illustrates exemplary simulation data corresponding to templatepopulation evolution as sequencing progresses for the flow ordering ofFIG. 14A.

FIG. 15A illustrates exemplary simulation data corresponding to signalresponse curves for an exemplary flow ordering of “TACG TACG TACG TACGTACG TACA TACG CACG TGCG TATG” (SEQ ID NO: 6).

FIG. 15B illustrates exemplary simulation data corresponding to templatepopulation evolution as sequencing progresses for the flow ordering ofFIG. 15A.

FIG. 16A illustrates exemplary simulation data corresponding to signalresponse curves for an exemplary flow ordering of “TACG TACG TCTG AGCATCGA TCGA TGTA CAGC” (SEQ ID NO: 7).

FIG. 16B illustrates exemplary simulation data corresponding to templatepopulation evolution as sequencing progresses for the flow ordering ofFIG. 16A.

FIG. 17A illustrates exemplary simulation data corresponding to signalresponse curves for an exemplary flow ordering of “TACG TACG TCTG AGCATCGA TCGA TGTA CAGC TGAC TGAC TATC GCAG AGCT AGCT ACAT GTCG ACTG ACTGATAG CGTC ATGC ATGC AGAC TCGT CGTA CGTA CTCA GATG CTAG CTAG CACG TGATCAGT CAGT CGCT ATGA GTCA GTCA GCGA TACT GCAT GCAT GAGT CTAC GATC GATCGTGC ACTA” (SEQ ID NO: 8).

FIG. 17B illustrates exemplary simulation data corresponding to templatepopulation evolution as sequencing progresses for the flow ordering ofFIG. 17A.

FIG. 18A illustrates exemplary simulation data corresponding to signalresponse curves for an exemplary random flow ordering of “CTTG CTTA CAACTCTC ATAT CGGT ATCC TGTG GAAA CTCC GTTA TCAG CATC CTCT CATG TTAG” (SEQID NO: 9).

FIG. 18B illustrates exemplary simulation data corresponding to templatepopulation evolution as sequencing progresses for the random flowordering of FIG. 18A.

FIG. 19A illustrates exemplary simulation data corresponding to signalresponse curves for an exemplary flow ordering of “TACA CTCT AGTA TAGAGTCG TGTC TCGA CGCG AGAC” (SEQ ID NO: 10).

FIG. 19B illustrates exemplary simulation data corresponding to templatepopulation evolution as sequencing progresses for the flow ordering ofFIG. 19A.

FIG. 20 illustrates an exemplary method for sequencing a nucleic acidusing phase-protecting flows.

FIG. 21 illustrates an exemplary system for nucleic acid sequencing.

EXEMPLARY EMBODIMENTS

The following description and the various embodiments described hereinare exemplary and explanatory only and are not to be construed aslimiting or restrictive in any way. Other embodiments, features,objects, and advantages of the present teachings will be apparent fromthe description and accompanying drawings, and from the claims.

In accordance with the teachings and principles embodied in thisapplication, new methods, systems, apparatuses, and computer readablemedia that perform sequencing-by-synthesis while reducing or minimizingsequencing errors associated with various phase loss effects that mayoccur with sequencing-by-synthesis are provided.

Unless otherwise specifically designated herein, terms, techniques, andsymbols of biochemistry, cell biology, genetics, molecular biology,nucleic acid chemistry, and organic chemistry (including, e.g., chemicaland physical analysis of polymer particles, nucleic acid sequencing andanalysis, polymerization techniques, preparation of syntheticpolynucleotides, recombinant techniques, etc.) used herein follow thoseof standard treatises and texts in the relevant field. See, e.g.,Kornberg and Baker, DNA REPLICATION, 2nd ed. (W.H. Freeman, New York,1992); Lehninger, BIOCHEMISTRY, 2nd ed. (Worth Publishers, New York,1975); Strachan and Read, HUMAN MOLECULAR GENETICS, 2nd ed. (Wiley-Liss,New York, 1999); Birren et al. (eds.), GENOME ANALYSIS: A LABORATORYMANUAL SERIES (Vols. I-IV), Dieffenbach and Dveksler (eds.), PCR PRIMER:A LABORATORY MANUAL, and Green and Sambrook (eds.), MOLECULAR CLONING: ALABORATORY MANUAL (all from Cold Spring Harbor Laboratory Press); andHermanson, BIOCONJUGAIE TECHNIQUES, 2nd ed. (Academic Press, 2008).

In this application, “amplifying” generally refers to performing anamplification reaction.

In this application, “amplicon” generally refers to a product of apolynucleotide amplification reaction, which includes a clonalpopulation of polynucleotides, which may be single stranded or doublestranded and which may be replicated from one or more startingsequences. The one or more starting sequences may be one or more copiesof the same sequence, or they may be a mixture of different sequencesthat contain a common region that is amplified such as, for example, aspecific exon sequence present in a mixture of DNA fragments extractedfrom a sample. Preferably, amplicons may be formed by the amplificationof a single starting sequence. Amplicons may be produced by a variety ofamplification reactions whose products comprise replicates of one ormore starting, or target, nucleic acids. Amplification reactionsproducing amplicons may be “template-driven” in that base pairing ofreactants, either nucleotides or oligonucleotides, have complements in atemplate polynucleotide that are required for the creation of reactionproducts. Template-driven reactions may be primer extensions with anucleic acid polymerase or oligonucleotide ligations with a nucleic acidligase. Such reactions include, for example, polymerase chain reactions(PCRs), linear polymerase reactions, nucleic acid sequence-basedamplifications (NASBAs), rolling circle amplifications, for example,including such reactions disclosed in one or more of Gelfand et al.,U.S. Pat. No. 5,210,015; Kacian et al., U.S. Pat. No. 5,399,491; Mullis,U.S. Pat. No. 4,683,202; Mullis et al., U.S. Pat. Nos. 4,683,195;4,965,188; and 4,800,159; Lizardi, U.S. Pat. No. 5,854,033; and Wittweret al., U.S. Pat. No. 6,174,670, which are all incorporated by referenceherein in their entirety. In an embodiment, amplicons may be produced byPCRs. Amplicons may also be generated using rolling circle amplificationto form a single body that may exclusively occupy a microwell asdisclosed in Drmanac et al., U.S. Pat. Appl. Publ. No. 2009/0137404,which is incorporated by reference herein in its entirety.

In this application, “solid phase amplicon” generally refers to a solidphase support, such as a particle or bead, to which is attached a clonalpopulation of nucleic acid sequences, which may have been produced by aprocess such as emulsion PCR, for example.

In this application, “analyte” generally refers to a molecule orbiological cell that can directly affect an electronic sensor in aregion (such as a defined space or reaction confinement region ormicrowell, for example) or that can indirectly affect such an electronicsensor by a by-product from a reaction involving such molecule orbiological cell located in such region. In an embodiment, an analyte maybe a sample or template nucleic acid, which may be subjected to asequencing reaction, which may, in turn, generate a reaction by-product,such as one or more hydrogen ions, that can affect an electronic sensor.The term “analyte” also comprehends multiple copies of analytes, such asproteins, peptides, nucleic acids, for example, attached to solidsupports, such as beads or particles, for example. In an embodiment, ananalyte may be a nucleic acid amplicon or a solid phase amplicon. Asample nucleic acid template may be associated with a surface viacovalent bonding or a specific binding or coupling reaction, and may bederived from, for example, a shot-gun fragmented DNA or amplicon library(which are examples of library fragments further discussed herein), or asample emulsion PCR process creating clonally-amplified sample nucleicacid templates on particles such as IonSphere™ particles. An analyte mayinclude particles having attached thereto clonal populations of DNAfragments, e.g., genomic DNA fragments, cDNA fragments, for example.

In this application, “primer” generally refers to an oligonucleotide,either natural or synthetic, that is capable, upon forming a duplex witha polynucleotide template, of acting as a point of initiation of nucleicacid synthesis and being extended from its 3′ end along the template sothat an extended duplex may be formed. Extension of a primer may becarried out with a nucleic acid polymerase, such as a DNA or RNApolymerase. The sequence of nucleotides added in the extension processmay be determined by the sequence of the template polynucleotide.Primers may have a length in the range of from 14 to 40 nucleotides, orin the range of from 18 to 36 nucleotides, for example, or from N to Mnucleotides where N is an integer larger than 18 and M is an integerlarger than N and smaller than 36, for example. Other lengths are ofcourse possible. Primers may be employed in a variety of amplificationreactions, including linear amplification reactions using a singleprimer, or polymerase chain reactions, employing two or more primers,for example. Guidance for selecting the lengths and sequences of primersfor particular applications may be found in Dieffenbach and Dveksler(eds.), PCR PRIMER: A LABORATORY MANUAL, 2nd ed. (Cold Spring HarborLaboratory Press, New York, 2003).

In this application, “polynucleotide” or “oligonucleotide” generallyrefers to a linear polymer of nucleotide monomers and may be DNA or RNA.Monomers making up polynucleotides are capable of specifically bindingto a natural polynucleotide by way of a regular pattern ofmonomer-to-monomer interactions, such as Watson-Crick type of basepairing, base stacking, Hoogsteen or reverse Hoogsteen types of basepairing, for example. Such monomers and their internucleosidic linkagesmay be naturally occurring or may be analogs thereof, e.g., naturallyoccurring or non-naturally occurring analogs. Non-naturally occurringanalogs may include PNAs, phosphorothioate internucleosidic linkages,bases containing linking groups permitting the attachment of labels,such as fluorophores, or haptens, for example. In an embodiment,oligonucleotide may refer to smaller polynucleotides, for example,having 5-40 monomeric units. Polynucleotides may include the naturaldeoxyribonucleosides (e.g., deoxyadenosine, deoxycytidine,deoxyguanosine, and deoxythymidine for DNA or their ribose counterpartsfor RNA) linked by phosphodiester linkages. However, they may alsoinclude non-natural nucleotide analogs, e.g., including modified bases,sugars, or internucleosidic linkages. In an embodiment, a polynucleotidemay be represented by a sequence of letters (upper or lower case), suchas “ATGCCTG,” and it will be understood that the nucleotides are in5′→3′ order from left to right and that “A” denotes deoxyadenosine, “C”denotes deoxycytidine, “G” denotes deoxyguanosine, and “T” denotesdeoxythymidine, and that “I” denotes deoxyinosine, and “U” denotesdeoxyuridine, unless otherwise indicated or obvious from context.Whenever the use of an oligonucleotide or polynucleotide requiresenzymatic processing, such as extension by a polymerase, ligation by aligase, or the like, one of ordinary skill would understand thatoligonucleotides or polynucleotides in those instances would not containcertain analogs of internucleosidic linkages, sugar moieties, or basesat any or some positions. Unless otherwise noted the terminology andatom numbering conventions will follow those disclosed in Strachan andRead, HUMAN MOLECULAR GENETICS, 2nd ed. (Wiley-Liss, New York, 1999).Polynucleotides may range in size from a few monomeric units, e.g.,5-40, to several thousand monomeric units, for example.

In this application, “defined space” (or “reaction space,” which may beused interchangeably with “defined space”) generally refers to any space(which may be in one, two, or three dimensions) in which at least someof a molecule, fluid, and/or solid can be confined, retained and/orlocalized. The space may be a predetermined area (which may be a flatarea) or volume, and may be defined, for example, by a depression or amicro-machined well in or associated with a microwell plate, microtiterplate, microplate, or a chip. The area or volume may also be determinedbased on an amount of fluid or solid, for example, deposited on an areaor in a volume otherwise defining a space. For example, isolatedhydrophobic areas on a generally hydrophobic surface may provide definedspaces. In an embodiment, a defined space may be a reaction chamber,such as a well or a microwell, which may be in a chip. In an embodiment,a defined space may be a substantially flat area on a substrate withoutwells, for example. A defined space may contain or be exposed to enzymesand reagents used in nucleotide incorporation.

In this application, “reaction confinement region” generally refers toany region in which a reaction may be confined and includes, forexample, a “reaction chamber,” a “well,” and a “microwell” (each ofwhich may be used interchangeably). A reaction confinement region mayinclude a region in which a physical or chemical attribute of a solidsubstrate can permit the localization of a reaction of interest, and adiscrete region of a surface of a substrate that can specifically bindan analyte of interest (such as a discrete region with oligonucleotidesor antibodies covalently linked to such surface), for example. Reactionconfinement regions may be hollow or have well-defined shapes andvolumes, which may be manufactured into a substrate. These latter typesof reaction confinement regions are referred to herein as microwells orreaction chambers, may be fabricated using any suitable microfabricationtechniques, and may have volume, shape, aspect ratio (e.g., basewidth-to-well depth ratio), and other dimensional characteristics thatmay be selected depending on particular applications, including thenature of reactions taking place as well as the reagents, by-products,and labeling techniques (if any) that are employed. Reaction confinementregions may also be substantially flat areas on a substrate withoutwells, for example. In various embodiments, microwells may be fabricatedas described in one or more of Doering and Nishi (eds.), HANDBOOK OFSEMICONDUCTOR MANUFACTURING TECHNOLOGY, 2nd ed. (CRC Press, 2007);Saliterman, FUNDAMENTALS OF BIOMEMS AND MEDICAL MICRODEVICES (SPIE PressBook, 2006); Elwenspoek et al., SILICON MICROMACHINING (CambridgeUniversity Press, 2004); and the like. Various exemplary configurations(e.g., spacing, shape, and volume) of microwells or reaction chambersare disclosed in Rothberg et al., U.S. Pat. Publ. Nos. 2009/0127589 and2009/0026082; Rothberg et al., U.K. Pat. Appl. Publ. No. GB 2461127; andKim et al., U.S. Pat. No. 7,785,862, which are all incorporated byreference in their entirety.

Defined spaces or reaction confinement regions may be arranged as anarray, which may be a substantially planar one-dimensional ortwo-dimensional arrangement of elements such as sensors or wells. Thenumber of columns (or rows) of a two-dimensional array may or may not bethe same. Preferably, the array comprises at least 100,000 chambers.Preferably, each reaction chamber has a horizontal width and a verticaldepth that has an aspect ratio of about 1:1 or less. Preferably, thepitch between the reaction chambers is no more than about 10 microns.Preferably, each reaction chamber is no greater than 10 μm³ (i.e., 1 pL)in volume, or no greater than 0.34 pL in volume, and more preferably nogreater than 0.096 pL or even 0.012 pL in volume. A reaction chamber maybe 2², 3², 4², 5², 6², 7², 8², 9², or 10² square microns incross-sectional area at the top, for example. Preferably, the array mayhave at least 10², 10³, 10⁴, 10⁵, 10⁶, 10⁷, 10⁸, 10⁹, or more reactionchambers, for example. The reaction chambers may be capacitively coupledto chemFETs. Microwells may have any polygonal cross sections, includingsquare, rectangular, or octagonal cross sections, for example, and maybe arranged as a rectilinear array on a surface. Microwells may havehexagonal cross sections and be arranged as a hexagonal array, whichpermits a higher density of microwells per unit area than rectilineararrays. An array of defined spaces or reaction confinement regions maybe an array of discrete areas on a substantially flat substrate withoutwells.

Defined spaces or reaction confinement regions, whether arranged as anarray or in some other configuration, may be in electrical communicationwith at least one sensor to allow detection or measurement of one ormore detectable or measurable parameter or characteristics. The sensorsmay convert changes in the presence, concentration, or amounts ofreaction by-products (or changes in ionic character of reactants) intoan output signal, which may be registered electronically, for example,as a change in a voltage level or a current level which, in turn, may beprocessed to extract information about a chemical reaction or desiredassociation event, for example, a nucleotide incorporation event. Thesensors may include at least one chemically sensitive field effecttransistor (“chemFET”) that can be configured to generate at least oneoutput signal related to a property of a chemical reaction or targetanalyte of interest in proximity thereof. Such properties can include aconcentration (or a change in concentration) of a reactant, product orby-product, or a value of a physical property (or a change in suchvalue), such as an ion concentration. An initial measurement orinterrogation of a pH for a defined space or reaction confinementregion, for example, may be represented as an electrical signal or avoltage, which may be digitalized (e.g., converted to a digitalrepresentation of the electrical signal or the voltage). Any of thesemeasurements and representations may be considered raw data or a rawsignal. The structure and/or design of sensors for use with the presentteachings may vary widely and may include one or more features of thefollowing references, which are all incorporated by reference herein intheir entirety: Barbaro et al., U.S. Pat. No. 7,535,232; Esfandyarpouret al., U.S. Pat. Appl. Publ. No. 2008/0166727; Kamahori et al., U.S.Pat. Appl. Publ. No. 2007/0059741; Miyahara et al., U.S. Pat. Appl.Publ. Nos. 2008/0286767 and 2008/0286762; O'uchi, U.S. Pat. Appl. Publ.No. 2006/0147983; Osaka et al., U.S. Pat. Appl. Publ. No. 2007/0207471;Rothberg et al., U.S. Pat. Appl. Publ. No. 2009/0127589; Rothberg etal., U.K. Pat. Appl. Publ. No. GB 2461127; and Sawada et al., U.S. Pat.No. 7,049,645.

In this application, “reaction mixture” generally refers to a solutioncontaining any necessary reactants for performing a reaction, which mayinclude, for example, buffering agents to maintain pH at a selectedlevel during a reaction, salts, enzymes, co-factors, scavengers, etc.,for example.

In this application, “microfluidics device” generally refers to anintegrated system of one or more chambers, ports, and channels that areinterconnected and in fluid communication and designed for carrying outan analytical reaction or process, either alone or in cooperation withan appliance or instrument that provides support functions, such assample introduction, fluid and/or reagent driving means, temperaturecontrol, detection systems, data collection and/or integration systems,etc. Microfluidics devices may further include valves, pumps, andspecialized functional coatings on interior walls, e.g., to preventadsorption of sample components or reactants, facilitate reagentmovement by electroosmosis, etc. Such devices may be fabricated usingmicromachining techniques or precision molding, for example, in or as asolid substrate, which may be glass, plastic, or other solid polymericmaterials, and may have a planar format for ease of detecting andmonitoring sample and reagent movement, especially via optical orelectrochemical methods. Features of a microfluidic device may havecross-sectional dimensions of less than a few hundred squaremicrometers, for example, and passages may have capillary dimensions,e.g., having maximal cross-sectional dimensions of from about 500 μm toabout 0.1 μm, for example. Microfluidics devices may have volumecapacities in the range of from 1 μL to a few nL, e.g., 10-100 nL, forexample.

In various embodiments, the methods, systems, apparatuses, and computerreadable media described herein may advantageously be used to determinethe sequence and/or identity of one or more nucleic acid samples usingsequencing-by-synthesis. In sequencing-by-synthesis, the sequence of atarget nucleic acid may be determined by the stepwise synthesis ofcomplementary nucleic acid strands on a target nucleic acid (whosesequence and/or identity is to be determined) serving as a template forthe synthesis reactions (e.g., by a polymerase extension reaction thattypically includes the formation of a complex comprising a template (ortarget polynucleotide), a primer annealed thereto, and a polymeraseoperably coupled or associated with the primer-template hybrid so as tobe capable of incorporating a nucleotide species (e.g., a nucleosidetriphosphate, a nucleotide triphosphate, a precursor nucleoside ornucleotide) to the primer). During sequencing-by-synthesis, nucleotidesmay be sequentially added to growing polynucleotide molecules or strandsat positions complementary to template polynucleotide molecules orstrands. The addition of the nucleotides to the growing complementarystrands, which may be detected using a variety of methods (e.g.,pyrosequencing, fluorescence detection, and label-free electronicdetection), may be used to identify the sequence composition of thetemplate nucleic acid. This process may be iterated until a complete orselected sequence length complementary to the template has beensynthesized.

In various embodiments, the methods, systems, apparatuses, and computerreadable media described herein may advantageously be used to generate,process, and/or analyze data and signals obtained using electronic orcharged-based nucleic acid sequencing. In electronic or charged-basedsequencing (such as, e.g., pH-based sequencing), a nucleotideincorporation event may be determined by detecting ions (e.g., hydrogenions) generated as natural by-products of polymerase-catalyzednucleotide extension reactions. This may be used to sequence a sample ortemplate nucleic acid, which may be a fragment of a nucleic acidsequence of interest, for example, and which may be directly orindirectly attached as a clonal population to a solid support, such as aparticle, microparticle, bead, etc. The sample or template nucleic acidmay be operably associated to a primer and polymerase and may besubjected to repeated cycles or “flows” of deoxynucleoside triphosphate(“dNTP”) addition (which may be referred to herein as “nucleotide flows”from which nucleotide incorporations may result) and washing. The primermay be annealed to the sample or template so that the primer's 3′ endcan be extended by a polymerase whenever dNTPs complementary to the nextbase in the template are added. Then, based on the known sequence ofnucleotide flows and on measured signals indicative of ion concentrationduring each nucleotide flow, the identity of the type, sequence andnumber of nucleotide(s) associated with a sample nucleic acid present ina reaction chamber can be determined.

FIG. 1 illustrates components of an exemplary system for nucleic acidsequencing. The components include a flow cell and sensor array 100, areference electrode 108, a plurality of reagents 114, a valve block 116,a wash solution 110, a valve 112, a fluidics controller 118, lines120/122/126, passages 104/109/111, a waste container 106, an arraycontroller 124, and a user interface 128. The flow cell and sensor array100 includes an inlet 102, an outlet 103, a microwell array 107, and aflow chamber 105 defining a flow path of reagents over the microwellarray 107. The reference electrode 108 may be of any suitable type orshape, including a concentric cylinder with a fluid passage or a wireinserted into a lumen of passage 111. The reagents 114 may be driventhrough the fluid pathways, valves, and flow cell by pumps, gaspressure, or other suitable methods, and may be discarded into the wastecontainer 106 after exiting the flow cell and sensor array 100. Thereagents 114 may, for example, contain dNTPs to be flowed throughpassages 130 and through the valve block 116, which may control the flowof the reagents 114 to flow chamber 105 (also referred to herein as areaction chamber) via passage 109. The system may include a reservoir110 for containing a wash solution that may be used to wash away dNTPs,for example, that may have previously been flowed. The microwell array107 may include an array of defined spaces or reaction confinementregions, such as microwells, for example, that is operationallyassociated with a sensor array so that, for example, each microwell hasa sensor suitable for detecting an analyte or reaction property ofinterest. The microwell array 107 may preferably be integrated with thesensor array as a single device or chip. The flow cell may have avariety of designs for controlling the path and flow rate of reagentsover the microwell array 107, and may be a microfluidics device. Thearray controller 124 may provide bias voltages and timing and controlsignals to the sensor, and collect and/or process output signals. Theuser interface 128 may display information from the flow cell and sensorarray 100 as well as instrument settings and controls, and allow a userto enter or set instrument settings and controls. The system may beconfigured to let a single fluid or reagent contact the referenceelectrode 108 throughout an entire multi-step reaction. The valve 112may be shut to prevent any wash solution 110 from flowing into passage109 as the reagents are flowing. Although the flow of wash solution maybe stopped, there may still be uninterrupted fluid and electricalcommunication between the reference electrode 108, passage 109, and thesensor array 107. The distance between the reference electrode 108 andthe junction between passages 109 and 111 may be selected so that littleor no amount of the reagents flowing in passage 109 and possiblydiffusing into passage 111 reach the reference electrode 108. In anembodiment, the wash solution 110 may be selected as being in continuouscontact with the reference electrode 108, which may be especially usefulfor multi-step reactions using frequent wash steps.

In various embodiments, the fluidics controller 118 may be programmed tocontrol driving forces for flowing reagents 114 and the operation ofvalve 112 and valve block 116 with any suitable instrument controlsoftware, such as LabView (National Instruments, Austin, Tex.), todeliver reagents to the flow cell and sensor array 100 according to apredetermined reagent flow ordering. The reagents may be delivered forpredetermined durations, at predetermined flow rates, and may measurephysical and/or chemical parameters providing information about thestatus of one or more reactions taking place in defined spaces orreaction confinement regions, such as, for example, microwells. Thepredetermined ordering may be based on a cyclical, repeating patternconsisting of consecutive repeats of a short pre-determined reagent flowordering (e.g., consecutive repeats of pre-determined sequence of fournucleotide reagents such as, for example, “ACTG ACTG ACTG . . . ”), maybe based in whole or in part on some other pattern of reagent flows(such as, e.g., any of the various phase-protecting reagent floworderings discussed herein), and may also be based on some combinationthereof.

FIG. 2A illustrates cross-sectional and expanded views of an exemplaryflow cell 200 for nucleic acid sequencing. The flow cell 200 includes amicrowell array 202, a sensor array 205, and a flow chamber 206 in whicha reagent flow 208 may move across a surface of the microwell array 202,over open ends of microwells in the microwell array 202. The flow ofreagents (e.g., nucleotide species) can be provided in any suitablemanner, including delivery by pipettes, or through tubes or passagesconnected to a flow chamber. The duration, concentration, and/or otherflow parameters may be the same or different for each reagent flow.Likewise, the duration, composition, and/or concentration for each washflow may be the same or different. A microwell 201 in the microwellarray 202 may have any suitable volume, shape, and aspect ratio, whichmay be selected depending on one or more of any reagents, by-products,and labeling techniques used, and the microwell 201 may be formed inlayer 210, for example, using any suitable microfabrication technique. Asensor 214 in the sensor array 205 may be an ion sensitive (ISFET) or achemical sensitive (chemFET) sensor with a floating gate 218 having asensor plate 220 separated from the microwell interior by a passivationlayer 216, and may be predominantly responsive to (and generate anoutput signal related to) an amount of charge 224 present on thepassivation layer 216 opposite of the sensor plate 220. Changes in theamount of charge 224 cause changes in the current between a source 221and a drain 222 of the sensor 214, which may be used directly to providea current-based output signal or indirectly with additional circuitry toprovide a voltage output signal. Reactants, wash solutions, and otherreagents may move into microwells primarily by diffusion 240. One ormore analytical reactions to identify or determine characteristics orproperties of an analyte of interest may be carried out in one or moremicrowells of the microwell array 202. Such reactions may generatedirectly or indirectly by-products that affect the amount of charge 224adjacent to the sensor plate 220. In an embodiment, a referenceelectrode 204 may be fluidly connected to the flow chamber 206 via aflow passage 203. In an embodiment, the microwell array 202 and thesensor array 205 may together form an integrated unit forming a bottomwall or floor of the flow cell 200. In an embodiment, one or more copiesof an analyte may be attached to a solid phase support 212, which mayinclude microparticles, nanoparticles, beads, gels, and may be solid andporous, for example. The analyte may include a nucleic acid analyte,including a single copy and multiple copies, and may be made, forexample, by rolling circle amplification (RCA), exponential RCA, orother suitable techniques to produce an amplicon without the need of asolid support.

FIG. 2B illustrates an exemplary uniform flow front between successivereagents moving across a section 234 of an exemplary microwell array. A“uniform flow front” between first reagent 232 and second reagent 230generally refers to the reagents undergoing little or no mixing as theymove, thereby keeping a boundary 236 between them narrow. The boundarymay be linear for flow cells having inlets and outlets at opposite endsof their flow chambers, or it may be curvilinear for flow cells havingcentral inlets (or outlets) and peripheral outlets (or inlets). In anembodiment, the flow cell design and reagent flow rate may be selectedso that each new reagent flow with a uniform flow front as it transitsthe flow chamber during a switch from one reagent to another.

FIG. 3A illustrates exemplary flow paths through a flow chamber havingdiagonally opposed inlet and outlet. The reagents may follow flow paths300 as they transit along a diagonal axis of the flow chamber between aninlet 302 and an outlet 304, which paths may not reach all the way tocorner 301, for example.

In an embodiment, a flow cell may direct reagent flows to an array ofmicrowells such that each microwell is exposed to substantially the sameflow conditions, such as flow rate and concentration, for example, atsubstantially the same time throughout the microwell array as reagentsare delivered to the array. (As used herein in reference to suchexposure, “substantially the same time” generally refers to the transittime through the flow chamber of a boundary between two successivereagents being small in comparison to the length of time a microwell isexposed to any one reagent.) In an embodiment, a flow cell may haveinlets and outlets located diagonally in a flow chamber constrained to arectilinear space, and in such a configuration achieving identical flowrates at each microwell may not be possible. Nonetheless, anydifferences in flow conditions experienced by different microwells, suchas flow rate, may then preferably be minimized by a flow chamber and theflow path it defines.

FIG. 3B illustrates an exemplary flow chamber 308 with an exemplarysensor array area defined by reference to a reach of reagent flow paths.The flow chamber may include an area covered by the reagents as theytransit from inlet 302 to outlet 304 (excluding an area 306 outside theboundary 307 that delimits an extent of the reagent flow reach in theflow chamber), which area may be used to locate microwells.

FIGS. 4A and 4B illustrate schematically an exemplary process forlabel-free, pH-based sequencing. A template 682 with sequence 685 and aprimer binding site 681 are attached to a solid phase support 680. Thetemplate 682 may be attached as a clonal population to a solid support,such as a microparticle or bead, for example, and may be prepared asdisclosed in Leamon et al., U.S. Pat. No. 7,323,305, which isincorporated by reference herein in its entirety. In an embodiment, thetemplate may be associated with a substrate surface or present in aliquid phase with or without being coupled to a support. A primer 684and DNA polymerase 686 are operably bound to the template 682. As usedherein, “operably bound” generally refers to a primer being annealed toa template so that the primer's 3′ end may be extended by a polymeraseand that a polymerase is bound to such primer-template duplex (or inclose proximity thereof) so that binding and/or extension may take placewhen dNTPs are added. In step 688, dNTP (shown as dATP) is added, andthe DNA polymerase 686 incorporates a nucleotide “A” (since “T” is thenext nucleotide in the template 682 and is complementary to the floweddATP nucleotide). In step 690, a wash is performed. In step 692, thenext dNTP (shown as dCTP) is added, and the DNA polymerase 686incorporates a nucleotide “C” (since “G” is the next nucleotide in thetemplate 682). The pH-based nucleic acid sequencing, in which baseincorporations may be determined by measuring hydrogen ions that aregenerated as natural by-products of polymerase-catalyzed extensionreactions, may be performed using at least in part one or more featuresof Anderson et al., A SYSTEM FOR MULTIPLEXED DIRECT ELECTRICAL DETECTIONOF DNA SYNTHESIS, Sensors and Actuators B: Chem., 129:79-86 (2008);Rothberg et al., U.S. Pat. Appl. Publ. No. 2009/0026082; and Pourmand etal., DIRECT ELECTRICAL DETECTION OF DNA SYNTHESIS, Proc. Natl. Acad.Sci., 103:6466-6470 (2006), which are all incorporated by referenceherein in their entirety. In an embodiment, after each addition of adNTP, an additional step may be performed in which the reaction chambersare treated with a dNTP-destroying agent, such as apyrase, to eliminateany residual dNTPs remaining in the chamber that might result inspurious extensions in subsequent cycles. FIG. 4B further illustratesvarious aspects of this process, while providing additional detailsregarding a first nucleotide incorporation (left) leading to a schematicsignal representing a single A incorporation, and a second incorporation(right) leading to a schematic signal representing a pair of Tincorporations.

In an embodiment, the primer-template-polymerase complex may besubjected to a series of exposures of different nucleotides in apre-determined sequence or ordering. If one or more nucleotides areincorporated, then the signal resulting from the incorporation reactionmay be detected, and after repeated cycles of nucleotide addition,primer extension, and signal acquisition, the nucleotide sequence of thetemplate strand may be determined. The output signals measuredthroughout this process depend on the number of nucleotideincorporations. Specifically, in each addition step, the polymeraseextends the primer by incorporating added dNTP only if the next base inthe template is complementary to the added dNTP. If there is onecomplementary base, there is one incorporation; if two, there are twoincorporations; if three, there are three incorporations, and so on.With each incorporation, an hydrogen ion is released, and collectively apopulation released hydrogen ions change the local pH of the reactionchamber. The production of hydrogen ions may be monotonically related tothe number of contiguous complementary bases in the template (as well asto the total number of template molecules with primer and polymerasethat participate in an extension reaction). Thus, when there is a numberof contiguous identical complementary bases in the template (which mayrepresent a homopolymer region), the number of hydrogen ions generatedand thus the magnitude of the local pH change is proportional to thenumber of contiguous identical complementary bases (and thecorresponding output signals are then sometimes referred to as “1-mer,”“2-mer,” “3-mer” output signals, etc.). If the next base in the templateis not complementary to the added dNTP, then no incorporation occurs andno hydrogen ion is released (and the output signal is then sometimesreferred to as a “0-mer” output signal). In each wash step of the cycle,an unbuffered wash solution at a predetermined pH may be used to removethe dNTP of the previous step in order to prevent misincorporations inlater cycles. In an embodiment, the four different kinds of dNTP areadded sequentially to the reaction chambers, so that each reaction isexposed to the four different dNTPs, one at a time. In an embodiment,the four different kinds of dNTP are added in the following sequence:dATP, dCTP, dGTP, dTTP, dATP, dCTP, dGTP, dTTP, etc., with eachexposure, incorporation, and detection steps followed by a wash step.Each exposure to a nucleotide followed by a washing step can beconsidered a “nucleotide flow.” Four consecutive nucleotide flows can beconsidered a “cycle.” For example, a two cycle nucleotide flow order canbe represented by: dATP, dCTP, dGTP, dTTP, dATP, dCTP, dGTP, dTTP, witheach exposure being followed by a wash step. Different flow orders areof course possible.

FIGS. 4C-4P illustrate schematically exemplary flow-based steps forsequencing a target using sequencing-by-synthesis. The example of targetillustrated here includes, for example, an A adapter, a sequencing keyor code (“AGTC” in this example), a sequence of interest (“ATTAC . . . ”in this example), and a P1 adapter attached to or associated with aparticle (for example). FIG. 4C illustrates a first flow of T nucleotidespecies, which leads to a single incorporation (a T “1-mer”) because thefirst available base is A, which is complementary. FIG. 4D illustrates asecond flow of A nucleotide species, which leads to no incorporation (anA “0-mer”) because the next available base is G, which is notcomplementary. FIG. 4E illustrates a third flow of C nucleotide species,which leads to a single incorporation (a C “1-mer”) because the nextavailable base is G, which is complementary. FIG. 4F illustrates afourth flow of G nucleotide species, which leads to no incorporation (aG “0-mer”) because the next available base is T, which is notcomplementary. FIG. 4G illustrates a fifth flow of T nucleotide species,which leads to no incorporation (a T “0-mer”) because the next availablebase is T, which is not complementary. FIG. 4H illustrates a sixth flowof A nucleotide species, which leads to a single incorporation (an A“1-mer”) because the next available base is T, which is complementary.FIG. 4I illustrates a seventh flow of C nucleotide species, which leadsto no incorporation (a C “0-mer”) because the next available base is C,which is not complementary. FIG. 4J illustrates an eighth flow of Gnucleotide species, which leads to a single incorporation (a G “1-mer”)because the next available base is C, which is complementary. FIG. 4Killustrates a ninth flow of T nucleotide species, which leads to asingle incorporation (a T “1-mer”) because the next available base is A,which is complementary. FIG. 4L illustrates a tenth flow of A nucleotidespecies, which leads to a double incorporation (an A “2-mer”) becausethe next two available bases are T, which are complementary. FIG. 4Millustrates an eleventh flow of C nucleotide species and a twelfth flowof G nucleotide species, which lead to no incorporation (C and G“0-mers”) because the next available base is A, which is notcomplementary. FIG. 4N illustrates a thirteenth flow of T nucleotidespecies, which leads to a single incorporation (a T “1-mer”) because thenext available base is A, which is complementary. FIG. 4O illustrates afourteenth flow of A nucleotide species and a fifteenth flow of Cnucleotide species, which lead to no incorporation (A and C “0-mers”)because the next available base is C, which is not complementary.Finally, FIG. 4P illustrates a sixteenth flow of G nucleotide species,which leads to a single incorporation (a G “1-mer”) because the nextavailable base is C, which is complementary. In each case, a signalproportional to the homopolymer length (e.g., 0, 1, 2, . . . ) is alsoillustrated. Although the flow ordering in the example of FIGS. 4C-4Pwas according to “TACG TACG . . . ,” other flows, such as any of thevarious phase-protecting reagent flow orderings discussed herein, couldalso be used.

FIG. 4Q illustrates exemplary raw pH-based sequencing data correspondingto counts associated with a plurality of nucleotide flows. In thisexample, the reagent flow ordering is “TACG TACG TCTG AGCA TCGA TCGATGTA CAGC” (SEQ ID NO: 7) (flowed in whole once and then followed by itsfirst eight flows). The counts on the y-axis are scaled values that maybe viewed as representative of a voltage output signal that shouldgenerally be proportional in magnitude to the number of nucleotideincorporations likely to have resulted in response to each of thevarious nucleotide flows. In other words, the signal should remain closeto the baseline for a 0-mer, should attain approximately 1 for a 1-mer,should attain approximately 2 for a 2-mer, should attain approximately 3for a 3-mer, and so on. The x-axis represents time.

FIG. 4R illustrates exemplary flow-by-flow numerical valuescorresponding to raw pH-based sequencing data from which homopolymerlength predictions can be made. For every particular flow (the type ofwhich is indicated by a circle for A, a square for C, a diamond for G,and a triangle for T), there corresponds a numerical value from whichhomopolymer length can be determined. In this example, the first flow ofT shows a value around 1, suggesting a single incorporation of T; thesecond flow of A shows a value around 0, suggesting no incorporation ofA, and so on. Based on knowledge of such predicted homopolymer lengthshaving resulted from each flow in the predetermined ordering of flows, alikely sequence of the target may be inferred.

In various embodiments, output signals due to nucleotide incorporationmay be processed in various way to improve their quality and/orsignal-to-noise ratio, which may include performing or implementing oneor more of the teachings disclosed in Rearick et al., U.S. patentapplication Ser. No. 13/339,846, filed Dec. 29, 2011, based on U.S.Prov. Pat. Appl. Nos. 61/428,743, filed Dec. 30, 2010, and 61/429,328,filed Jan. 3, 2011, and in Hubbell, U.S. patent application Ser. No.13/339,753, filed Dec. 29, 2011, based on U.S. Prov. Pat. Appl. No.61/428,097, filed Dec. 29, 2010, which are all incorporated by referenceherein in their entirety.

In various embodiments, output signals due to nucleotide incorporationmay be further processed, given knowledge of what nucleotide specieswere flowed and in what order to obtain such signals, to make base callsfor the flows and compile consecutive base calls associated with asample nucleic acid template into a read. A base call refers to aparticular nucleotide identification (e.g., dATP (“A”), dCTP (“C”), dGTP(“G”), or dTTP (“T”)). Base calling may include performing one or moresignal normalizations, signal phase and signal droop (e.g., enzymeefficiency loss) estimations, and signal corrections, and may identifyor estimate base calls for each flow for each defined space. Basecalling may include performing or implementing one or more of theteachings disclosed in Davey et al., U.S. patent application Ser. No.13/283,320, filed Oct. 27, 2011, based on U.S. Prov. Pat. Appl. No.61/407,377, filed on Oct. 27, 2010, which are both incorporated byreference herein in their entirety. Other aspects of signal processingand base calling may include performing or implementing one or more ofthe teachings disclosed in Davey et al., U.S. patent application Ser.No. 13/340,490, filed on Dec. 29, 2011, based on U.S. Prov. Pat. Appl.No. 61/428,733, filed on Dec. 30, 2010, which are all incorporated byreference herein in their entirety.

The accuracy of sequencing and the efficiency with which sequencing maybe performed can be impacted by several types of sequencing errors thatmay arise when using sequencing-by-synthesis. Some of these errors arerelated to synchrony issues. Specifically, a large population ofsubstantially identical template strands (e.g., 10³ to 10⁷ molecules)may be analyzed substantially simultaneously in a given sequencingreaction to obtain sufficiently distinct and resolvable signals forreliable detection in sequencing-by-synthesis, and it is desirable thatsynthesis for the strands proceed in step or in phasic synchrony witheach other. Signal-to-noise ratios may be improved when there ishomogeneous and/or contemporaneous extension of the complementary strandassociated with the template molecules in a population. Each extensionreaction associated with the population of template molecules may bedescribed as being generally “in phase” or in “phasic synchrony” witheach other when they are performing the same incorporation step at thesame sequence position for the associated template molecules in a givenreaction step. It has been observed, however, that a relatively smallfraction of template molecules in each population may lose or fall outof phasic synchrony (e.g., may become “out of phase”) with the majorityof the template molecules in the population. That is, the incorporationevents associated with a certain fraction of template molecules mayeither get ahead of or fall behind other similar template molecules inthe sequencing run. Such phase loss effects are described in Ronaghi,GENOME RESEARCH, 11:3-11 (2001); Leamon et al., CHEMICAL REVIEWS,107:3367-3376 (2007); Chen et al., International Publ. No. WO2007/098049.

One such phase loss effect relates to an “incomplete extension” (IE)event or error. An IE event may occur as a result of a failure of asequencing reaction to incorporate one or more nucleotide species intoone or more nascent molecules for a given extension round of thesequence, for example, which may result in subsequent reactions being ata sequence position that is out of phase with the sequence position forthe majority of the population (e.g., certain template extensions fallbehind the main template population). IE events may arise, for example,because of a lack of nucleotide availability to a portion of thetemplate/polymerase complexes of a population, or because of a failureof a portion of the polymerase molecules to incorporate a nucleotideinto a complementary strand at the appropriate time, because of a lossof polymerase activity, or because of some other relevant cause orfactor.

Another such phase loss effect relates to a “carry forward” (CF) eventor error. A CF event may occur as a result of an improper extension of anascent molecule by incorporation of one or more nucleotide species in asequence or strand position that is ahead and out of phase with thesequence or strand position of the rest of the population. CF events mayarise, for example, because of the misincorporation of a nucleotidespecies, or in certain instances, because of contamination or excessnucleotides remaining from a previous cycle (e.g., which may result froman insufficient or incomplete washing of the reaction chamber). Forexample, a small fraction of a “T” nucleotide cycle may be present orcarry forward to a “C” nucleotide cycle. The presence of bothnucleotides may lead to an undesirable extension of a fraction of thegrowing strands where the “T” nucleotide is incorporated in addition tothe “C” nucleotide such that multiple different nucleotideincorporations events take place where only a single type of nucleotideincorporation would normally be expected. CF events may also arisebecause of a polymerase error (e.g., there may be an improperincorporation of a nucleotide species into the nascent molecule that isnot complementary to the nucleotide species on the template molecule).

FIG. 5 illustrates exemplary IE and CF events that may occur and resultin loss of phasic synchrony during sequencing-by-synthesis. It showsthree DNA duplexes. For each duplex, the bottom row of boxes representsthe template polynucleotide strand 32 and the top row of boxesrepresents the complementary extension strand 30 being extended by apolymerase. The extension strand includes the primer portion, asindicated by the bar. The ()-filled boxes indicate the incorporation ofcomplementary nucleotides. The top DNA duplex (labeled “in-phase”)represents members of the population that are in the correct phase. Themiddle DNA duplex (labeled “IE”) represents a portion of the populationthat has experienced an omission at the C nucleotide (an IE error). Thebottom DNA duplex (labeled “CF”) represents a portion of the populationthat has experienced an erroneous incorporation at the G nucleotide (aCF error).

Errors or phasing issues related to IE and CF events may be exacerbatedover time because of the accumulation of such events, which may causedegradation of sequence signal or quality over time and an overallreduction in the practical read length of the system (e.g., the numberof nucleotides that can be sequenced for a given template). The presentteachings reflect the discovery that sequencing performance (e.g.,efficiency and/or accuracy of sequencing) may be affected by theparticular composition, nature, and sequence of nucleotides delivered tosequencing-by-synthesis reactions.

According to various embodiments, there are provided methods, systems,apparatuses, and computer readable media for performingsequencing-by-synthesis while reducing or minimizing sequencing errorsassociated with the aforementioned phase loss effects that may occurwith sequencing-by-synthesis. The methods, systems, apparatuses, andcomputer readable media may include steps and/or structural elements forperforming sequencing-by-synthesis using reagents that are flowedaccording to a predetermined ordering. Although the predeterminedordering may be based on a cyclical, repeating pattern consisting ofconsecutive repeats of a short pre-determined reagent flow ordering(e.g., consecutive repeats of a pre-determined sequences of fournucleotide reagents, for example), the predetermined ordering mayadvantageously comprise in whole or in part a phase-protecting reagentflow ordering as described herein.

FIG. 6A illustrates an exemplary system for obtaining, processing,and/or analyzing nucleic acid sequencing data. The system includes asequencing instrument 601, a server 602 or other computing means orresource, and one or more end user computers 605 or other computingmeans or resource. The sequencing instrument 601 may be configured todeliver reagents according to a predetermined ordering, which may bebased on a cyclical, repeating pattern consisting of consecutive repeatsof a short pre-determined reagent flow ordering (e.g., consecutiverepeats of pre-determined sequence of four nucleotide reagents such as“TACG TACG . . . ”), or may be based on an ordering comprising in wholeor in part a phase-protecting reagent flow ordering as described herein,or some combination thereof. The server 602 may include a processor 603and a memory and/or database 604. The sequencing instrument 601 and theserver 602 may include one or more computer readable media forobtaining, processing, and/or analyzing nucleic acid sequencing data. Inan embodiment, the instrument and the server or other computing means orresource may be configured as a single component. One or more of thesecomponents may be used to perform or implement one or more aspects ofthe embodiments described herein.

FIG. 6B illustrates an exemplary method for obtaining, processing,and/or analyzing nucleic acid sequencing data. In step 611, a userobtains physical sequencing data from an instrument configured to use,at least in part, one or more phase-protecting reagent flow orderings.The physical sequencing data may include voltage data indicative ofhydrogen ion concentrations, for example, and may be based on acyclical, repeating pattern consisting of consecutive repeats of a shortpre-determined reagent flow ordering (e.g., consecutive repeats ofpre-determined sequence of four nucleotide reagents such as “TACG TACG .. . ”), or may be based on an ordering comprising in whole or in part aphase-protecting reagent flow ordering as described herein, or somecombination thereof, for example. In step 612, a server or othercomputing means or resource converts the physical sequencing data intosequences of bases. In step 613, the server or other computing means orresource delivers the physical sequencing data and/or sequences of basesto an end user. One or more of these steps and/or components may be usedto perform or implement one or more aspects of the embodiments describedherein.

In an embodiment, a predetermined permutation of four distinct reagentflows (e.g., any of the possible 4-flow permutations of A, C, T, and G,such as ACTG, CATG, GATC, or CTAG, for example) may be repeatedlydelivered (flowed) consecutively and always in the same order. Forexample, the first nucleotide delivered may be dATP, then dCTP, thendGTP, then dTTP (or a permutation thereof), after which this sequence offour nucleotides (which may be called a “cycle”) may be repeated anynumber of times consecutively. Deliveries of nucleotides to a reactionvessel or chamber may be referred to as “flows” of nucleotidetriphosphates (or dNTPs). For convenience, a flow of dATP will sometimesbe referred to as “a flow of A” or “an A flow,” and a sequence of flowsmay be represented as a sequence of letters, such as “ATGT” indicating“a flow of dATP, followed by a flow of dTTP, followed by a flow of dGTP,followed by a flow of dTTP.” In each flow, a polymerase may generallyextend the primer by incorporating the flowed dNTP where the next basein the template strand is the complement of the flowed dNTP. When usingsuch cyclical, consecutively repeating flows, however, out-of-synctemplates generally will not be given an opportunity to resynchronizewith the in-sync population, which may lead to phase-related sequencingerrors. Further, while such cyclical, consecutively repeating flows canbe generally efficient at extending sequence obtained per flow, as thenext unknown base is guaranteed to be resolved within three flows of thepresent flow, such an approach may be problematic as such flow ordersprovide no opportunities for phase-protection.

According to various embodiments, sequencing-by-synthesis reactions maybe performed using a flow ordering comprising in whole or in part aphase-protecting reagent flow ordering, which may help reduce and/orcorrect the loss of phasic synchrony in the population of templatepolynucleotide strands that may result from IE and/or CF events. Inparticular, such flow orderings may give out-of-sync templates anopportunity to resynchronize (move into the same phase or re-sync) withthe in-sync population in order to change the way the templatepopulation evolves, which may in turn reduce the fraction of out-of-synctemplates in the population and/or counteract the accumulated dephasingof templates. In other words, such flow orderings may at least partiallysuspend progression of a main population of templates being sequencedand allow at least a portion of the out of phase population to catch upLikewise, for out of phase sequences that have progressed ahead of themain population such flow orderings may at least partially suspendprogression of the out of phase population and allow at least a portionof the main population to catch up. In some embodiments, such flows maybe used not to completely remove or alleviate dephasing, but rather as amechanism to balance or reduce accumulated dephasing effects while atthe same time maintaining an efficient or desirable number of flows toachieve a selected/expected throughput (e.g., the flows used to sequencea respective template length). Thus, such flows may result in areduction and/or correction of CF and/or IE events, improvement inphasic synchrony, increased signal-to-noise ratio, base callingaccuracy, and/or overall read length of a sequencing run.

In various embodiments, a phase-protecting reagent flow ordering may bea flow ordering that (1) is not a series of consecutive repeats of a4-flow permutation of four different reagents (e.g., “ACTG ACTG . . . ”or “CAGT CAGT . . . ” for example) and (2) is not specifically tailoredto a particular combination of a particular template polynucleotidestrand to be sequenced and a particular sequencing primer to be used.More specifically, in such embodiments, the flow ordering is not aseries of consecutive repeats of any one of the 4!=24 possible 4-flowpermutations of four given reagents (e.g., dNTPs or any other relevantreagents for performing sequencing-by-synthesis reactions), is notspecifically tailored to a particular template polynucleotide strand tobe sequenced, and is not specifically tailored to a particularsequencing primer to be used, so that the phase-protecting reagent flowordering may have broad applicability to any templates or at least toclasses of templates that may share some common properties.

In various embodiments, a phase-protecting reagent flow ordering may bederived from a flow ordering that is a series of consecutive repeats ofa 4-flow permutation of four different reagents (e.g., “ACTG ACTG . . .” or “CAGT CAGT . . . ” for example) by introducing one or more reagentchanges into the sequence (e.g., “ACAG ACTG” or “CACT CAGT” where onechange, shown in boldface and underlining, is made relative to “ACTGACTG . . . ” or “CAGT CAGT . . . ”). More generally, 2, 3, 4, 5, 10, 15,20, or more changes could be made from such consecutive series, and aphase-protecting reagent flow ordering may thus be a substantiallynon-cyclical, non-repeating pattern of reagents.

In various embodiments, a phase-protecting reagent flow ordering may be“TACT CAGT ATGC AGAC TGCG” (SEQ ID NO: 11), “TACG TACG TACT CAGC TAGCTAGT ATGC ATGC ATGC AGAC TGAC TGAC TGCG” (SEQ ID NO: 12), “TACG TACGTACT CAGC TAGT ATGC ATGC AGAC TGAC TGCG” (SEQ ID NO: 13), “TACG TACGTTAC TCAG CTAA GTAT GCAT GGCA GACT GACC TGCG” (SEQ ID NO: 14), “TACGTACG TCTG AGCA TCGA TCGA TGTA CAGC” (SEQ ID NO: 7), “TACG TACG TACG TACGTACG TACA TACG CACG TGCG TATG” (SEQ ID NO: 6), “TACG TACG TACG TACG TACGTACAT ACGCA CGTGC GTATG” (SEQ ID NO: 2), and “TACG TACG TAGC TGAC GTACGTCA TGCA TCGA TCAG CTAG CTGA CGTA GCTA GCAT CGAT CAGT CATG ACTG ACGTAGCT GACT GATC AGTC ATGC ATCG” (SEQ ID NO: 5), for example. Other floworderings are, of course, possible. (Note: To facilitate readability,lengthy flow orderings may sometimes be listed using groups of flowsseparated by spaces (e.g., “TACG TACG” rather than “TACGTACG”); however,the presence of the spaces does not have any particular meaning orsignificance other than to facilitate readability).

In various embodiments, a phase-protecting reagent flow ordering may bederived from a set of k-ary de Bruijn sequences B(k,n), where k denotesa size of an alphabet (e.g., k may be set to 4 for an alphabetcomprising the nucleotide species A, C, G, and T), and where n denotes alength of subsequences in the alphabet. The sequence(s) B(k,n) is/aresuch that every possible subsequence of length n in the alphabet appearsexactly once as a sequence of consecutive characters. The de Bruijnapproach to flow order determination desirably provides efficient waysto sequence through all four bases while covering potential dimers andgenerally providing good uncorrelated base flow characteristics. As anexample, for an alphabet A={0, 1}, there is a single B(2, 2) sequence,“0011”, and there are two distinct B(2, 3) sequences, “00010111” and“11101000,” each of which being the reverse and/or negation of theother. More information about de Bruijn sequences and related conceptsmay be found in Ehrenfest and de Bruijn, CIRCUITS AND TREES IN ORIENTEDLINEAR GRAPHS, Simon Stevin, 28:203-217 (1951); de Bruijn,ACKOWLEDGEMENT OF PRIORITY TO C. FLYE SAINTE-MARIE ON THE COUNTING OFCIRCULAR ARRANGEMENTS OF 2^(N) ZEROS AND ONES THAT SHOW EACH N-LETTERWORD EXACTLY ONCE, T.H.-Report 75-WSK-06, Technological UniversityEindhoven (1975); and Berstel and Perrin, THE ORIGINS OF COMBINATRONICSON WORDS, European Journal of Combinatronics, 28:996-1022 (2007), whichare all incorporated by reference herein in their entirety. In variousembodiments, a phase-protecting reagent flow ordering may be a de Bruijnsequence of the nucleotide species A, C, G, and T (an alphabet with fourmembers) where n=2 or where n=3, without any consecutive repeats of thesame nucleotide species. In an embodiment, a phase-protecting reagentflow ordering may be an ordering comprising “TACG TCTG AGCA” (SEQ ID NO:15). In an embodiment, a phase-protecting reagent flow ordering may be aKautz sequence, which is a de Bruijn sequence that does not have anyconsecutive repeats of the same character.

In various embodiments, a phase-protecting reagent flow ordering may bederived so as to comprise all possible distinct dimer pairs of fourreagents (e.g., nucleotide species A, C, G, and T, where “distinct” withrespect to a pair generally refers to the nucleotide species making upthe pair being different from each other). For example, the ordering mayinclude the 12 distinct dimer pairs of A, C, G, and T (which are AG, AC,AT, CA, CG, CT, GA, GC, GT, TA, TC, and TG). Although joining each ofthe 12 distinct dimer pairs together, one after the other, would lead toa 24-flow sequence, constructing a flow sequence containing all 12distinct pairs does not necessarily require a 24-flow sequence. Shorterflow sequences may be constructed by overlapping at least some of thedimers. For example, the 6-flow sequence AGCATC includes the pairs AG,GC, CA, AT, and TC. In an embodiment, such a flow ordering may be a deBruijn sequence-based flow ordering that comprises substantially alldistinct pairs in 12 bases. For example, the 12-flow sequence “TACG TCTGAGCA” (SEQ ID NO: 15) contains all 12 distinct pairs appearing exactlyonce (with the AT pair occurring in the wrap-around when the sequence isrepeated), and provides the ability to sequence through all fournucleotides while at the same time providing desirable dephasingproperties. The 12 distinct pairs may be contained in longer flowsequences. For example, the 32-flow sequence “TACG TACG TCTG AGCA TCGATCGA TGTA CAGC” (SEQ ID NO: 7) contains each of the 12 distinct dimerpairs. This modification may advantageously be applied in the context ofun-terminated sequencing reactions as repeated bases (e.g.,homopolymers) will typically not be sequenced in separate sequentialflows but rather within the same flow corresponding to thehomopolymetric nucleotide.

In various embodiments, a phase-protecting reagent flow ordering mayinclude a flow ordering in which at least one base (e.g., “T”) isfollowed by a different base (e.g., “G”, “C”, or “A”) in at least twodifferent ways in the ordering (e.g., the ordering includes at least twoof “TG”, “TC”, and “TA”). In other words, such a flow ordering mayinclude a flow of N followed immediately by a flow of X, where X and Nare variables representing different nucleotide species, while furtherincluding, immediately thereafter or elsewhere in the ordering, anotherflow of N followed immediately by a flow of Y, where Y is a variablerepresenting a nucleotide species different from both X and N. Forexample, such a flow ordering may contain the following flow sequence:“TG . . . TC . . . TA”. In another embodiment, such a flow ordering mayinclude a flow of X followed immediately by a flow of N, where X and Nare variables representing different nucleotide species, while furtherincluding, immediately thereafter or elsewhere in the ordering, a flowof Y followed immediately by the flow of N, where Y is a variablerepresenting a nucleotide species different from both X and N. Forexample, such a flow ordering may be “TACG TACG TACG TACG TACG TACG TACGCACGTGCGTATG” (SEQ ID NO: 16) where several cycles of TACG floworderings are followed by an ordering that includes CG and TG in whichthe G nucleotide flow is preceded by C and T (note that this orderingalso includes AC and GC, GT and AT, and CA and TA, which also followthis pattern).

In various embodiments, a phase-protecting reagent flow ordering mayinclude an ordering in which three of the four nucleotide species A, C,G, and T are flowed at least twice before the fourth nucleotide speciesis flowed. For example, the flow sequence “TACTACG” repeats each of T,A, and C before the fourth nucleotide species G is flowed. In anotherexample, the flow sequence “TACATACG” repeats T twice, C twice, and Athree times before the fourth nucleotide G is flowed. In this approach,the flow ordering starves the template population of the fourthnucleotide species. This starvation of the fourth nucleotide species mayresult in many or most of the template population awaiting the fourthnucleotide for incorporation, thus giving an opportunity forresynchronization of the template population with the flow of the fourthnucleotide. Other examples of “starvation” flow orderings include (withthe starved nucleotides underlined): a 20-flow sequence with aG-starvation, then a C-starvation, and then a T-starvation(“TACTCAGTATGCAGACTGCG” (SEQ ID NO: 11)); a 40-flow sequence (“TACG TACGTACTCAG CTAGTATGC ATGCAGACT GACTGCG” (SEQ ID NO: 17)), and a 52-flowsequence (“TACG TACG TACTCAG CTAGC TAGTATGC ATGCAT GCAGACT GACTGACTGCG”(SEQ ID NO: 12)), for example. Each of the four nucleotide species A, C,G, and T may alternate as the starved nucleotide. For example, the flowsequence “TACATACG” may be used to starve the population of G, followedby the flow sequence “ACGACGT” to starve the population of T, followedby the flow sequence “TAGTAGC” to starve the population of C, and thenfollowed by the flow sequence “CGTCGTA” to starve the population of A.This embodiment in which the template population is starved of each ofthe four different nucleotides species in turn may be accomplished inany suitable number of flows, including, e.g., a 20-flow sequence(allowing some overlapping of one flow set to another). In anembodiment, such a flow ordering may not include one of each of the fournucleotides in sequential repetition and may include intervening flowswhere one or more nucleotide flows are delivered multiple times prior todelivery of all four nucleotides in the flow sequence (e.g., such a flowordering may be “TCTA GACT CGAG” (SEQ ID NO: 18)).

In various embodiments, a phase-protecting reagent flow ordering mayinclude a first set of flows and a second set of flows, with the secondset of flows being derived from a remapping of the nucleotide species inthe first set of flows. The remapping may involve nucleotides of oneparticular species in the first set of flows (e.g., all the A's or allthe C's) being assigned to a different nucleotide species to generatethe flow ordering for the second set of flows. This remapping mayinvolve the reassignment of all or less than all instances of thenucleotide species in the first set of flows. There may be a remappingof two or more of the types of nucleotide species in the first set offlows. Because it is derived from a remapping, such a second set offlows is different from the first set of flows. For example, a first setof flows may be “TACG TCTG AGCA” (SEQ ID NO: 15) and a second set offlows may be created by reassigning nucleotide species as follows: G→A,C→G, and A→C for each instance of the nucleotide species in the firstset of flows. By this remapping, the second set of flows becomes “TCGATGTA CAGC” (SEQ ID NO: 19). In another example, “TACG TACG TCTG AGCATCGA TCGA TGTA CAGC” (SEQ ID NO: 7) consists of a first set of sixteenflows followed by a second set of sixteen flows, which is generated bythe following remapping assignments: G→A, C→G, and A→C. In variousembodiments, such flow orderings may contain additional sets of flowsbased on further remappings. For example, there may be a third set offlows derived from a remapping of the first or second set of flows.

Such embodiments of flow orderings based on flow remapping may beparticularly useful when used with flow orderings having resynchronizingproperties because the resynchronizing properties are preserved in thesecond set of flows, but the diversity of the overall flow ordering isincreased. For example, if the first set of flows is a de Bruijnsequence having resynchronizing properties, then the second set of flowsresulting from a remapping will also be a de Bruijin sequence havingresynchronizing properties, but with a different flow order. As aresult, repetition of the same flow ordering is reduced and overalldiversity of the flow order is increased. Increasing the diversity ofthe flow ordering may further enhance the resynchronizing properties ofthe flow ordering. For example, without the additional diversityprovided by, e.g., remapping, some fraction of the template populationmay fall into an out-of-sync phase that is in a stable, offset alignmentfrom the in-sync phase. This stable population of out-of-sync templatesmay accumulate at offsets that are multiples of the repeating flowordering cycle. Being in a stable, offset alignment from the in-syncpopulation, this particular out-of-sync population may never have theopportunity to catch up or become synchronized to the in-syncpopulation. But increasing the diversity of the flow ordering, e.g., byremapping, may impede the ability of stable populations of out-of-synctemplates to evolve.

According to various embodiments, flow orderings may include one or moreof the above-described flow patterns. For example, such a flow orderingmay be “TACAT ACGCA CGTGC GTATG” (SEQ ID NO: 20), which has several ofthe above-described flow patterns. Specifically, this ordering hasremapping features: the second 5-flow set is a remapping of the first5-flow set in which T→A, A→C, and C→G; the third 5-flow set is aremapping of the second 5-flow set with A→C, C→G, and G→T; and thefourth 5-flow set is a remapping of the third 5-flow set with C→G, G→T,and T→A. It also includes subsequences in which a flow of nucleotidespecies N is followed by a flow of a different nucleotide species X,which is followed by a flow of N again, which is then followed by a flowof Y that is a different nucleotide species from X and N (in particular,the subsequences ACAT, CGCA, GTGC, and TATG follow this pattern). And italso includes a pattern in which the population is starved of the Gnucleotide, then starved of the T nucleotide, and then starved of the Anucleotide.

In various embodiments, a phase-protecting reagent flow ordering may beconstructed using combinatorial optimization means. For example, onemight construct a flow ordering containing all 24 possible 4-flowpermutations of nucleotide species A, C, G, and T in succession, withthe differences between adjacent permutation 4-flow blocks being minimalin some metric (for example, guaranteeing that no nucleotide species iscloser than 3 flows or further than 5 flows away). Such a sampleconstraint may be achieved by requiring that adjacent permutation blocksdiffer only by a single transposition of two nucleotide species. Each ofthe 24 4-flow permutations may be represented by a vertex in a graph,and an edge may be inserted between any two vertices if thecorresponding permutations differ by a single transposition. A flowordering containing these permutation blocks then corresponds to a pathin this graph, and a flow ordering containing all 24 permutationsexactly once and returning to the starting permutation is then aHamiltonian path or circuit in this graph. Finding a Hamiltoniancircuit, as in this example, allows the construction of a flow orderthat is highly diverse among permutations, while maintaining goodefficiency of extending sequence. The CONTRADANZON flow orderingmentioned herein is an example of an ordering constructed for the mostpart using such a combinatorial optimization approach (although thatparticular ordering includes slight modifications allowing use ofcertain key sequences).

In various embodiments, any phase-protecting reagent flow ordering asdescribed herein may have a minimum length (e.g., in number of flows),which may be 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,39, 40, 45, 50, etc., or more generally which may be any positiveinteger larger than 4. In some embodiments, a flow ordering may berepeated in whole or part to complete a sequencing run and/or attain adesired minimum length.

In various embodiments, flow orderings may include a combination of aplurality of different phase-protecting flow orderings and/or acombination of one or more phase-protecting flow orderings with one ormore other flow orderings (e.g., consecutive repeats of a pre-determinedpermutation of four different reagents) so as to form a longer flowordering of a desired length and/or to balance properties of differenttypes of flow orderings. Such flow orderings may include a flow of onekind followed by a flow of a different kind, and both flows may havesame or different lengths. Such flow orderings may have subsequences offlow orderings that are repeated throughout a run to make up a desiredtotal number of flows. Such a flow ordering may comprise a 20-base flow(e.g., “TACT CAGT ATGC AGAC TGCG” (SEQ ID NO: 11)), for example, whichmay be repeated one or more times to achieve a desired number of flows,a 40-base flow (e.g., “TACG TACG TACT CAGC TAGT ATGC ATGC AGAC TGACTGCG” (SEQ ID NO: 13)), or a 52-base flow (e.g., “TACG TACG TACT CAGCTAGC TAGT ATGC ATGC ATGC AGAC TGAC TGAC TGCG” (SEQ ID NO: 12)), forexample. Other flow orderings may include flows having a partialcyclical 4-base flow repeated one or more times followed by another flowsequence of a different ordering, such as “TACG TACG TCTGAGCA TCGA TCGATGTACAGC” (SEQ ID NO: 7), “TACG TACG TACG TACG TACG TACA TACGCACGTGCGTATG” (SEQ ID NO: 21), and “TACG TACG TACG TACG TACG TACAT ACGCACGTGC GTATG” (SEQ ID NO: 2), for example. Such mixed flows may helpbalance efficiency (e.g., in terms of the total number of base flowsrequired to sequence a given length of template) versus the benefitgained (e.g., in terms of correct for or preventing phasing issue).Other flow orderings may include flows that sequentially alternatebetween two different types of orderings. Other flow orderings mayinclude longer sequence base flows, such as the 96-base flow “TACG TACGTAGC TGAC GTAC GTCA TGCA TCGA TCAG CTAG CTGA CGTA GCTA GCAT CGAT CAGTCATG ACTG ACGT AGCT GACT GATC AGTC ATGC ATCG” (SEQ ID NO: 5), forexample. In some embodiments, respective nucleotide flows may have thesame duration, relative concentration of nucleotide, and may be followedby an equivalent wash flow. In some embodiments, durations of differentnucleotide flows may be different, concentrations of differentnucleotide flows may be different, and durations and/or compositions ofintervening washes may be different. In some embodiments, the use ofphase-protecting flow orderings may be triggered or increased inresponse to detection of CF and/or IE events (e.g., in real-time, suchas when a detected level or frequency of CF and/or IE events has reacheda certain threshold). In some embodiments, such a use may be variedaccording to the position in the sequence read (e.g., use ofphase-protecting flow orderings may be triggered or increased after acertain read length of the sequence or may generally be used morefrequently at later stages of the sequence read), which may be useful ininstances where the CF and/or IE events increase at later stages of theread or in longer reads.

In various embodiments, a phase-protecting reagent flow ordering may beassociated or appended to a key sequence, such as TACG. The key sequencemay be appended to a de Bruijn sequence, where the key sequence will beexpected to demonstrate good signal resolution properties and efficientsequencing while the de Bruijn portion will be expected to providedesirable dephasing properties while sequencing through relatively longportions of a template. Additional details of key sequence usage aredescribed in U.S. Prov. Pat. Appl. No. 61/428,733, filed Dec. 30, 2010,U.S. patent application Ser. No. 13/340,490, filed Dec. 29, 2011, andU.S. Prov. Pat. Appl. No. 61/438,432, filed Feb. 1, 2011, which are allincorporated by reference herein in their entirety.

In various embodiments, a phase-protecting reagent flow ordering may bemodified to include one or more contiguous repetitions of the samereagent. For example, a nucleotide species may be flowed twice inimmediate succession, e.g., AA, TT, etc. For example, the flow sequence“TACG TACG TTAC TCAG CTAA GTAT GCAT GGCA GACT GACC TGCG” (SEQ ID NO: 14)contains the duplicates TT, AA, GG, and CC (which may be referred toherein as “double-tapped nucleotides”). Although there may be little orno actual incorporation of a nucleotide with an immediate repetition ofthe same nucleotide flow, the repeated nucleotide flow may be useful forestablishing a baseline signal (e.g., noise or background) absent anincorporation event. Further, interposing such repeated nucleotide flowsthroughout a sequencing run (e.g., every 50 or 100 flows) may furtherprovide the ability to monitor for changes in the reaction conditions(e.g., changes in buffering capacity or baseline, hydrogen ionaccumulation, evaluation of “bulk” ion present in solution absentnucleotide incorporation, etc.) over time and to identify sources ofsystematic error or faults. However, such “double-tapping” orderings mayor may not counteract the accumulated dephasing of templates.

It will be appreciated that achieving or improving phasic synchronydesirably enhances the ability to identify nucleotide incorporations andmore efficiently and/or accurately sequence templates. Although in manysequencing applications dephasing issues may be relatively small earlyin the sequencing run, their effects may accumulate as the sequencingprogresses and result in degraded sequencing quality for longertemplates. In practice, it will be appreciated that the correctiveeffect of flow orderings described herein will desirably enhanceefficiency and/or accuracy of sequencing by helping reduce or eliminatespurious signals associated with out-of-phase templates. Variousembodiments of flow orderings described herein may improve the overallquality of a sequencing run by increasing the number of individual readsthat achieve a desired sequencing quality, which may be represented asthe number of actual or expected errors over a series of bases. Forexample, error reporting may take the form of a quality scoring metricthat indicates the expected number of reads that achieve a desiredaccuracy or error rate over 50 or 100 base stretches. Flow orderings asdescribed herein may also be used to check or compare system performanceand for purposes of evaluating signal processing, base calling, andother algorithms (such as with “double-tapping” flows, for example).

FIG. 7A illustrates exemplary simulation data corresponding to signalresponse curves for an exemplary cyclical, repeating flow ordering of“GATC GATC . . . .” It shows signal response curves with signalintensity on the y-axis and the nth flow number (time) on the x-axis,and displays three triplet sets of plot lines, each of the triplet setshaving a darker solid line (40, 50, 60) in the middle between twolighter dotted lines (42, 52, 62; 44, 54, 64). The bottom-most tripletset of plot lines (60, 62, 64) show the signal from 0-mer events(non-incorporation); the middle triplet set of plot lines (50, 52, 54)show the signal from 1-mer incorporation events; and the top-mosttriplet set of plot lines (40, 42, 44) show the signal from 2-merincorporation events. Within each triplet set, the darker solid line inthe middle (40, 50, 60) represents the median signal, the lighter dottedline above (42, 52, 62) represents the 25 percentile signal, and thelighter dotted line below (44, 54, 64) represents the 75 percentilesignal. As shown in FIG. 7A, while the signal for the 1-mer and 2-merincorporation events degrades as the sequencing read progresses, thesignal produced by non-incorporation 0-mer events (e.g., the backgroundsignal) increases as the sequencing read progresses. Thus, at laterportions of the sequencing read, the signal resolution diminishes and itbecomes more difficult to distinguish the 0-mer, 1-mer, and 2-mer eventsfrom each other. As explained above, the accumulated effects of IE andCF events contribute to this degradation of signal quality.

FIG. 7B illustrates exemplary simulation data corresponding to templatepopulation evolution as sequencing progresses for the cyclical,repeating flow ordering of FIG. 7A. The y-axis represents the populationfraction, with the upper plot line representing the largest population(in-sync) and the lower plot line representing the second largestpopulation (out-of-sync). As shown in FIG. 7B, the relative number ofin-sync templates decreases while the relative number of out-of-synctemplates increases with progression of the sequencing read due to theloss of phase synchrony.

FIGS. 8A and 8B illustrate exemplary simulation data of the same type asin FIGS. 7A and 7B, but corresponding to signal response curves for anexemplary phase-protecting flow ordering of “TACG TACG TACG TACG TACGTACAT ACGCA CGTGC GTATG” (SEQ ID NO: 2). Similarly, FIGS. 9A and 9Billustrate exemplary simulation data of the same type as in FIGS. 7A and7B, but corresponding to signal response curves for an exemplaryphase-protecting flow ordering of “TACG TACG TCTG AGCA” (SEQ ID NO: 3).FIGS. 8A and 9A show that using the phase-protecting flow orderingsimproves signal resolution/separation and maintains signal intensitiesin the main population over a greater number of flows, when compared tothe flow ordering of FIG. 7A. In turn, FIGS. 8B and 9B show that thephase-protecting flow orderings slow the rate at which the out-of-phasepopulation accumulates, when compared to the flow ordering of FIG. 7B.In other words, the phase-protecting flow orderings help prevent themore rapid convergence of the main population and the two lesserpopulations associated with an increase in the out of phase populationdue to accumulated effects of unmitigated IE and/or CF related errors,and help provide better signal separation between the differentpopulations over time/flows and maintain a greater proportion of themain population (in phase) with greater signal intensity overtime/flows.

FIG. 10A illustrates an exemplary adjacency matrix representation forthe cyclical, repeating flow ordering of “TACG TACG . . . .” The matrixhas eight row and eight columns, corresponding to two cycles of TACG.Each row represents the possible flows where a base may incorporateafter the flow corresponding to a row. For example, the first rowcorresponds to the first T in the flow order, and the three coloredcells indicate the possible flows (ACG) where a sequence incorporatingin flow one may continue. The second row corresponds to the second flow“A”, and the colored blocks correspond to flows that may incorporateimmediately after incorporating an A in flow 2. Each column represents aflow where a growing sequence may continue to incorporate bases. Thereare four colors (red, green, blue, and purple) or shades of grey, andeach represents the base corresponding to each row (the base a growingsequence just incorporated a homopolymer run). Each vertical arrowrepresents the possible incorporation of a base at the correspondingflow, which would then be directed to the row where building a sequencemay continue. For example, the first vertical arrow in column tworepresents the fact that if a base were incorporated at the second flow,an “A”, the possible flows where the next base may incorporate are inthe second row; the second vertical arrow in column three represents thefact that if a base were incorporated at the third flow, a “C”, thepossible next flows where an incorporation may happen are the coloredblocks in the third row; etc. In this way, the color or shade or grey ofa block corresponds to the nucleotide previously incorporated in agrowing sequence, and the columns of the colored blocks indicatepotential other flows where a sequence may continue. Uncolored blocksare impossible to reach as the successor of an incorporation—forexample, the fifth flow, a “T”, may not be the first base (first row)incorporating after the first “T” flow. The properties of an adjacencymatrix are connected with the efficiency and phase-correcting propertiesof a flow ordering. In an embodiment, such a matrix representation maybe used to illustrate the efficiency and phase-correcting properties (orlack thereof) of a flow ordering. In particular, good efficiency andphase-correcting properties may be associated with the presence of atleast one color or shade or gray (or corresponding base type) that isrepeated in one or more columns of the matrix. Flow orderings possessingthis property may recombine out-of-phase molecules (although not allsuch flow orderings necessarily will recombine out-of-phase molecules).FIG. 10A does not exhibit this property (as every column has at mostthree bases that are distinct).

FIG. 10B illustrates an exemplary adjacency matrix representation forthe flow ordering of FIG. 9A. The matrix has thirty-two rows andthirty-two columns, corresponding to two repetitions of flow ordering“TACG TACG TCTG AGCA” (SEQ ID NO: 3). It shows six columns with repeats(see arrows) at a relatively high frequency and separated by relativelysmall gaps. For example, column 13 shows that there are two differentways of reaching this flow (an “A”) from a previous incorporationcontaining each of the other three bases; column 15 shows that there aretwo different ways of reaching this flow (a “C”) from previous “G”flows; etc. If there is a sequence with prefix ending in “GC”, twopopulations of molecules that are out of phase—one incorporating the “G”in one flow, one incorporating the “G” in the other, may become in phaseat the “C” flow, because both previous “G” flows have this “C” flow asthe successor. The corresponding flow ordering is thus likely to havegood efficiency and phase-correcting properties.

FIG. 10C illustrates an exemplary adjacency matrix representation forthe flow ordering of FIG. 8A. The matrix has eighty rows and eightycolumns, corresponding to two repetitions of flow ordering “TACG TACGTACG TACG TACG TACAT ACGCA CGTGC GTATG” (SEQ ID NO: 2). It shows eightcolumns with repeats (see arrows) arranged in two groups separated by agap of 20 bases. For example, column 25 shows that there are multipleways of incorporating a base in this flow, no matter what previous baseincorporated; column 28 shows that there are two ways of getting to thisflow from an “A”, etc. The corresponding flow ordering is thus alsolikely to have good efficiency and phase-correcting properties.

In various embodiments, there are provided methods for evaluating and/orranking flow orderings (e.g., phase-protecting flow orderings) toidentify most suitable ones. In an embodiment, flow orderings may beevaluated and/or ranked based on trade-offs between variouscharacteristics. Two examples of useful characteristics for this purposeare the extension efficiency (that is, some assessment of how rapidly asequence can be extended by a homopolymer) and the dephasing merit (thatis, some estimate of the ability of a particular flow ordering tominimize the effects of phasing issues on sequencing). The extensionefficiency may be relatively easy to assess. For example, it could bedetermined according to the expected number of homopolymers extended ina sequence after performing a given number of flows. For example, if theexpected number of homopolymers were 50 at flow 100, the efficiencycould be set to 0.5. Various other linear and non-linear approachescould also be used to assign efficiency to extension. A higherefficiency essentially signifies that sequencing may be performed fasterand at lower cost. In turn, the dephasing merit may be estimated bylooking at the realized separation between signals for a known 1-mer ina flow and signals for a known 0-mer in the flow (which would of coursebe occurring in different sequences). If these signals are reliablydistinct, the potential to reconstruct the sequence may be deemed high.If the distributions for 1-mers and 0-mers overlap, however, thepotential to reconstruct the sequence may be deemed low. One way ofsummarizing this relationship between distributions is to look at thedifference in median signal for each distribution, scaled by somemeasure of the variation (e.g., the interquartile range). This providesa picture of the dephasing effect in a given flow. (Note: to preventinstability when the population interquartile range is very small, asmall stabilizing noise estimate of 0.1 may be added, which was done inthe plotted figures). Because this measure can be variable per flow, andbecause the same flow may correspond to different expected sequencelengths given the different efficiencies of extension, it may beadvantageous to measure merit over many flows and over flowscorresponding to a range of expected sequence lengths. Finally, invarious embodiments, because these quantities/characteristics may bedifficult to obtain analytically, they may be assessed or examined bysimulation to evaluate what flow orders are likely to be most effective.

In various embodiments, phase-protecting reagent flow orderings may besimulated using various models related to IE and/or CF events. Forexample, such simulations may include one or more aspects described inU.S. patent application Ser. No. 13/283,320, filed Oct. 27, 2011, basedon U.S. Prov. Pat. Appl. No. 61/407,377, filed Oct. 27, 2010, which areall incorporated by reference herein in their entirety.

FIG. 11 illustrates an exemplary graph showing trade-offs betweenefficiency of extension and dephasing merit for eight exemplary floworderings. It shows simulated performance for eight particular floworderings (referred to as REGULAR, SAMBA, CD_DBTAP, CONTRADANZON,TANGO_HYBRID, SAMBA.GAFIEIRA, SLOWSEQ, and RANDOM64 herein) used against500 random sequences of length 300 drawn from a uniform distribution ofthe four bases. In all cases, the flow orderings are evaluated over aspan of 960 flows. The efficiency of extension over the first half ofthe sequence is evaluated by fitting a linear model and the dephasingmerit is computed over flows corresponding to 150 to 200 homopolymerextensions. The SAMBA flow represents a particularly good compromisebetween dephasing effectiveness and efficiency of extension. Otherrelatively similar flows are SAMBA.GAFIEIRA, TANGO_HYBRID, CD_DBTAP, andCONTRADANZON. A randomly chosen sequence (RANDOM64) shows that a highdegree of randomness is associated with excellent phase-protection(albeit at the cost of relatively low efficiency of extension). Asequence deliberately designed to increase dephasing at the expense ofextension efficiency (SLOWSEQ), shows a very high degree ofphase-protection. Although a sequence deliberately designed to achieve ahigh dephasing merit can outperform randomly chosen sequences for agiven extension efficiency, generally one must trade off one quality forthe other and an analysis of these the dephasing merit and efficiency ofextension characteristics provides a useful approach to evaluate and/orrank flow orderings for their suitability. In various embodiments, inorder to ensure optimal applicability of phase-protecting flow orderingsin as many contexts and applications as possible, the evaluation and/orranking of flow orderings may be based on a plurality of arbitrary orrandom test sequences and, in particular, the evaluation and/or rankingof flow orderings may be not tailored to any particular sequence to besequenced and/or primer to be used in such sequencing.

In various embodiments, the dephasing merit and efficiency of extensioncharacteristics may not be the only criteria, and other desirableproperties for flow orderings may be considered. For example,double-tapping flows have the added benefit of allowing directestimation of buffering in a given flow, as they provide a snapshot ofthe system without a significant amount of incorporation. In anotherexample, for effective variant detection, it may be desired to maximizeflow space diversity, which may be helpful when comparing multiplereads. In other examples, balancing usage of the nucleotide tubes andminimizing the time since a previous flow of a nucleotide can be helpfulproperties (in this regard, CONTRADANZON, for example, has no repeatednucleotides occurring more than five flows apart). Finally, in otherexamples specific applications and underlying biologic principlespertaining to certain classes of sequences may be taken intoconsideration (e.g., organisms with unusual GC content or enzymes withdiffering behaviors may benefit from use of flow orderings withdifferent likelihoods of sequences for the simulation, which may befactored in this flow ordering selection analysis) although at the costof some loss in optimally broad applicability. In various embodiments,phase-protecting reagent flow orderings may be selected to have as higha diversity of flows as possible. In various embodiments,phase-protecting reagent flow orderings may be selected to have as lowan auto-correlation as possible.

FIG. 12A illustrates exemplary simulation data corresponding to signalresponse curves for an exemplary cyclical, repeating flow ordering of“TACG TACG . . . .” FIG. 12B illustrates exemplary simulation datacorresponding to template population evolution as sequencing progressesfor the cyclical, repeating flow ordering of FIG. 12A. Except for thechange in flow ordering, the curves and plots in FIGS. 12A and 12B areof the same type as in FIGS. 7A and 7B. FIG. 12A shows that while thesignal for the 1-mer and 2-mer incorporation events degrades as thesequencing read progresses, the signal produced by non-incorporationO-mer events (e.g., the background signal) increases as the sequencingread progresses. Thus, at later portions of the sequencing read, thesignal resolution diminishes and it becomes more difficult todistinguish the 0-mer, 1-mer, and 2-mer events from each other. FIG. 12Bshows that the relative number of in-sync templates decreases while therelative number of out-of-sync templates increases with progression ofthe sequencing read due to the loss of phase synchrony.

FIG. 13A illustrates exemplary simulation data corresponding to signalresponse curves for an exemplary flow ordering of “TACG TACG TAGC TTGACGTA CGTC ATGC ATCG ATCA GCTA AGCT GACG TAGC TAGC ATCG ATCC AGTC ATGACTGA CGTA GCTG ACTG GATC AGTC ATGC ATCG” (SEQ ID NO: 4) (CD_DBTAP). FIG.13B illustrates exemplary simulation data corresponding to templatepopulation evolution as sequencing progresses for the flow ordering ofFIG. 13A. FIG. 14A illustrates exemplary simulation data correspondingto signal response curves for an exemplary flow ordering of “TACG TACGTAGC TGAC GTAC GTCA TGCA TCGA TCAG CTAG CTGA CGTA GCTA GCAT CGAT CAGTCATG ACTG ACGT AGCT GACT GATC AGTC ATGC ATCG” (SEQ ID NO: 5)(CONTRADANZON). FIG. 14B illustrates exemplary simulation datacorresponding to template population evolution as sequencing progressesfor the flow ordering of FIG. 14A. FIG. 15A illustrates exemplarysimulation data corresponding to signal response curves for an exemplaryflow ordering of “TACG TACG TACG TACG TACG TACA TACG CACG TGCG TATG”(SEQ ID NO: 6) (TANGO_HYBRID). FIG. 15B illustrates exemplary simulationdata corresponding to template population evolution as sequencingprogresses for the flow ordering of FIG. 15A. FIG. 16A illustratesexemplary simulation data corresponding to signal response curves for anexemplary flow ordering of “TACG TACG TCTG AGCA TCGA TCGA TGTA CAGC”(SEQ ID NO: 7) (SAMBA). FIG. 16B illustrates exemplary simulation datacorresponding to template population evolution as sequencing progressesfor the flow ordering of FIG. 16A. FIG. 17A illustrates exemplarysimulation data corresponding to signal response curves for an exemplaryflow ordering of “TACG TACG TCTG AGCA TCGA TCGA TGTA CAGC TGAC TGAC TATCGCAG AGCT AGCT ACAT GTCG ACTG ACTG ATAG CGTC ATGC ATGC AGAC TCGT CGTACGTA CTCA GATG CTAG CTAG CACG TGAT CAGT CAGT CGCT ATGA GTCA GTCA GCGATACT GCAT GCAT GAGT CTAC GATC GATC GTGC ACTA” (SEQ ID NO: 8)(SAMBA.GAFIEIRA). FIG. 17B illustrates exemplary simulation datacorresponding to template population evolution as sequencing progressesfor the flow ordering of FIG. 17A. FIG. 18A illustrates exemplarysimulation data corresponding to signal response curves for an exemplaryrandom flow ordering of “CTTG CTTA CAAC TCTC ATAT CGGT ATCC TGTG GAAACTCC GTTA TCAG CATC CTCT CATG TTAG” (SEQ ID NO: 9) (RANDOM64). FIG. 18Billustrates exemplary simulation data corresponding to templatepopulation evolution as sequencing progresses for the random flowordering of FIG. 18A. FIG. 19A illustrates exemplary simulation datacorresponding to signal response curves for an exemplary flow orderingof “TACA CTCT AGTA TAGA GTCG TGTC TCGA CGCG AGAC” (SEQ ID NO: 10)(SLOWSEQ). FIG. 19B illustrates exemplary simulation data correspondingto template population evolution as sequencing progresses for the flowordering of FIG. 19A. Except for the change in flow ordering, the curvesand plots in FIGS. 13A-19B are of the same type as in FIGS. 7A and 7B.These figures, when considered in comparison with the cyclical,repeating flow ordering of FIGS. 12A and 12B, show how phase-protectingflow orderings facilitate signal resolution/separation and help enhanceaccuracy of sequencing, especially with increasing numbers of flows.

In various embodiments, phase-protecting flow orderings may be used inthe context of paired-end sequencing. For example, a template sequencemight be sequenced twice, e.g., once in the forward direction and oncein the reverse, and may undergo incorporation for certain flows in theflow order in the forward direction (e.g., base 13 and base 14 mightundergo incorporation in flows 25 and 26). In such a case, it may beimpossible for a different base to be inserted between these two flows,which may provide strong evidence that there is no such insertion in thesequence. In the reverse direction, these two bases may be in flows thatare separated (e.g., say in flows 175 and 179), in which case thereverse read may be reconstructed to have an insertion between those twoflows. The forward read can correct such an error, however, because iteliminates certain classes of errors. It is therefore advantageous tohave the maximum number of opportunities where the successive flowsincorporating in the forward sequencing pass and the successive flowsincorporating in the reverse sequencing pass are different. Because thesequence cannot be known ahead of time, it is advantageous to select aflow ordering that maximizes the diversity of flows between a sequenceand the reverse complement of a sequence. One way of doing this is toengineer a flow ordering having many locally diverse patches, such asthe SAMBA.GAFIEIRA flow ordering, for example, to make it unlikely thata sequence being read in the forward and reverse directions willencounter similar succeeding flows.

FIG. 20 illustrates an exemplary method for sequencing a nucleic acidusing phase-protecting flows according to an embodiment. In step 2001, aplurality of template polynucleotide strands are disposed in a pluralityof defined spaces disposed on a sensor array, at least some of thetemplate polynucleotide strands having a sequencing primer and apolymerase operably bound therewith. In step 2002, the templatepolynucleotide strands with the sequencing primer and a polymeraseoperably bound therewith are exposed to a series of flows of nucleotidespecies flowed according to a predetermined ordering, wherein thepredetermined ordering (a) is not a series of consecutive repetitions ofa 4-flow permutation of four different nucleotide species, (b) is notspecifically tailored to a particular combination of a particulartemplate polynucleotide strand to be sequenced and a particularsequencing primer to be used, and (c) comprises a phase-protecting flowordering. In step 2003, it is determined, for each of the series offlows of nucleotide species, how many nucleotide incorporations occurredfor that particular flow to determine a predicted sequence ofnucleotides corresponding to the template polynucleotide strands.

FIG. 21 illustrates a system 2101 for nucleic acid sequencing accordingto an exemplary embodiment. The system includes a reactor array 2102; areader board 2103; a computer and/or server 2104, which includes a CPU2105 and a memory 2106; and a display 2107, which may be internal and/orexternal. One or more of these components may be used to perform orimplement one or more aspects of the exemplary embodiments describedherein.

According to an embodiment, there is provided a method for nucleic acidsequencing, comprising: (1) disposing a plurality of templatepolynucleotide strands in a plurality of defined spaces disposed on asensor array, at least some of the template polynucleotide strandshaving a sequencing primer and a polymerase operably bound therewith;(2) exposing the template polynucleotide strands with the sequencingprimer and a polymerase operably bound therewith to a series of flows ofnucleotide species flowed according to a predetermined ordering; and (3)determining, for each of the series of flows of nucleotide species, howmany nucleotide incorporations occurred for that particular flow todetermine a predicted sequence of nucleotides corresponding to thetemplate polynucleotide strands, wherein the predetermined ordering (a)is not a series of consecutive repetitions of a 4-flow permutation offour different nucleotide species, (b) is not specifically tailored to aparticular combination of a particular template polynucleotide strand tobe sequenced and a particular sequencing primer to be used, and (c)comprises a phase-protecting flow ordering.

In such a method, the phase-protecting flow ordering may comprise a deBruijn sequence of four predetermined nucleotide species having a deBruijn subsequence length parameter of two or three and without anyconsecutive repeats of the same nucleotide species. The de Bruijnsubsequence length parameter may be two. The de Bruijn subsequencelength parameter may be three. The predetermined ordering may comprise aportion that is a de Bruijn sequence and a portion that is not a deBruijn sequence. The four nucleotide species may be A, C, G, and T, andthe predetermined ordering may consist of only the phase-protecting flowordering. The de Bruijn subsequence ordering may be “TACG TCTG AGCA”(SEQ ID NO: 15). The phase-protecting flow ordering may comprise a flowordering that includes all possible distinct dimer pairs of fournucleotide species. The phase-protecting flow ordering may comprise aflow of N followed immediately by a flow of X, where X and N representdifferent nucleotide species, and further comprise, immediatelythereafter or elsewhere in the ordering, a flow of N followedimmediately by a flow of Y, where Y represents a nucleotide speciesdifferent from both X and N. The phase-protecting flow ordering maycomprise a flow of X followed immediately by a flow of N, where X and Nrepresent different nucleotide species, and further comprise a flow of Yfollowed immediately by a flow of N, where Y represents a nucleotidespecies different from both X and N. The phase-protecting flow orderingmay comprise a first flow ordering in which a first nucleotide species,a second nucleotide species, and a third nucleotide species are flowedat least twice before a fourth nucleotide species is flowed. Thephase-protecting flow ordering may further comprise a second flowordering in which the second nucleotide species, the third nucleotidespecies, and the fourth nucleotide species are flowed at least twicebefore the first nucleotide species is flowed. The phase-protecting flowordering may further comprise a third flow ordering in which the firstnucleotide species, the third nucleotide species, and the fourthnucleotide species are flowed at least twice before the secondnucleotide species is flowed. The phase-protecting flow ordering mayfurther comprise a fourth flow ordering in which the first nucleotidespecies, the second nucleotide species, and the fourth nucleotidespecies are flowed at least twice before the third nucleotide species isflowed. The phase-protecting flow ordering may comprise a first set offlows and a second set of flows, the second set of flows being derivedfrom a remapping of two or more of four nucleotide species flowed in thefirst set of flows. The second set of flows may be derived from aremapping of all four of the nucleotide species in the first set offlows. The phase-protecting flow ordering may comprise a flow orderingin which at least one given nucleotide species is contiguously flowedtwo or more times. The predetermined ordering may be selected based onan assessment of dephasing merit and efficiency of extension calculatedfor a plurality of candidate flow orderings using simulation sequencingdata obtained for a plurality of random test sequences. The sensor arraymay be configured to detect hydrogen ions released by incorporation ofnucleotides. The sensor array may be configured to detect inorganicpyrophosphate released by incorporation of nucleotides.

According to an embodiment, there is provided a system for nucleic acidsequencing, comprising: a machine-readable memory; and a processorconfigured to execute machine-readable instructions, which, whenexecuted by the processor, cause the system to perform steps including:exposing a plurality of template polynucleotide strands in a pluralityof defined spaces disposed on a sensor array, at least some of thetemplate polynucleotide strands having a sequencing primer and apolymerase operably bound therewith, to a series of flows of nucleotidespecies flowed according to a predetermined ordering; and determining,for each of the series of flows of nucleotide species, how manynucleotide incorporations occurred for that particular flow to determinea predicted sequence of nucleotides corresponding to the templatepolynucleotide strands, wherein the predetermined ordering (a) is not aseries of consecutive repetitions of a 4-flow permutation of fourdifferent nucleotide species, (b) is not specifically tailored to aparticular combination of a particular template polynucleotide strand tobe sequenced and a particular sequencing primer to be used, and (c)comprises a phase-protecting flow ordering.

In such a system, the phase-protecting flow ordering may comprise a deBruijn sequence of four predetermined nucleotide species having a deBruijn subsequence length parameter of two or three and without anyconsecutive repeats of the same nucleotide species. The phase-protectingflow ordering may comprise a flow ordering that includes all possibledistinct dimer pairs of four nucleotide species. The phase-protectingflow ordering may comprise a flow of N followed immediately by a flow ofX, where X and N represent different nucleotide species, and furthercomprise, immediately thereafter or elsewhere in the ordering, a flow ofN followed immediately by a flow of Y, where Y represents a nucleotidespecies different from both X and N. The phase-protecting flow orderingmay comprise a flow of X followed immediately by a flow of N, where Xand N represent different nucleotide species, and further comprise aflow of Y followed immediately by a flow of N, where Y represents anucleotide species different from both X and N. The phase-protectingflow ordering may comprise a first flow ordering in which a firstnucleotide species, a second nucleotide species, and a third nucleotidespecies are flowed at least twice before a fourth nucleotide species isflowed. The phase-protecting flow ordering may further comprise a secondflow ordering in which the second nucleotide species, the thirdnucleotide species, and the fourth nucleotide species are flowed atleast twice before the first nucleotide species is flowed. Thephase-protecting flow ordering may further comprise a third flowordering in which the first nucleotide species, the third nucleotidespecies, and the fourth nucleotide species are flowed at least twicebefore the second nucleotide species is flowed. The phase-protectingflow ordering may further comprise a fourth flow ordering in which thefirst nucleotide species, the second nucleotide species, and the fourthnucleotide species are flowed at least twice before the third nucleotidespecies is flowed. The phase-protecting flow ordering may comprise afirst set of flows and a second set of flows, the second set of flowsbeing derived from a remapping of two or more of four nucleotide speciesflowed in the first set of flows. The phase-protecting flow ordering maycomprise a flow ordering in which at least one given nucleotide speciesis contiguously flowed two or more times. The predetermined ordering maybe selected based on an assessment of dephasing merit and efficiency ofextension calculated for a plurality of candidate flow orderings usingsimulation sequencing data obtained for a plurality of random testsequences. The sensor array may be configured to detect hydrogen ionsreleased by incorporation of nucleotides. The sensor array may beconfigured to detect inorganic pyrophosphate released by incorporationof nucleotides.

According to an embodiment, there is provided a non-transitorymachine-readable storage medium comprising instructions which, whenexecuted by a processor, cause the processor to perform a method fornucleic acid sequencing comprising: exposing a plurality of templatepolynucleotide strands in a plurality of defined spaces disposed on asensor array, at least some of the template polynucleotide strandshaving a sequencing primer and a polymerase operably bound therewith, toa series of flows of nucleotide species flowed according to apredetermined ordering; and determining, for each of the series of flowsof nucleotide species, how many nucleotide incorporations occurred forthat particular flow to determine a predicted sequence of nucleotidescorresponding to the template polynucleotide strands, wherein thepredetermined ordering (a) is not a series of consecutive repetitions ofa 4-flow permutation of four different nucleotide species, (b) is notspecifically tailored to a particular combination of a particulartemplate polynucleotide strand to be sequenced and a particularsequencing primer to be used, and (c) comprises a phase-protecting flowordering.

According to an embodiment, there is provided a method for performingtemplate-based extension of primers, comprising: (a) providing at leastone template having a primer and polymerase operably associated thereto;and (b) successively exposing the templates to nucleotides in aplurality of flows such that nucleotides are not flowed in a strictlysequential and successive four nucleotide ordering (e.g., “TACG TACG . .. ” or “GATC GATC . . . ” or “ACTC ACTC . . . ” etc.).

According to an embodiment, there is provided an apparatus forsequencing a polynucleotide strand, comprising: a flow chamberconfigured to receive flows of different nucleotide species; a pluralityof reservoirs that each contain a different nucleotide species; aplurality of flow paths from each of the reservoirs to the flow chamber;and a fluidics controller configured to control the flow from thereservoirs to the flow chamber so as to flow nucleotide species from thereservoirs to the flow chamber according to a predetermined ordering ofnucleotide species comprising a phase-protecting flow ordering. Invarious embodiments, the apparatus may comprise a flow cell loaded intothe flow chamber, and the flow cell may comprise a microwell arraycontaining multiple copies of the polynucleotide strand with a primerannealed thereto. The flow cell may comprise a chemFET sensor array fordetecting the reaction of the nucleotides with the contents of themicrowell array. The polynucleotide strand may be attached to a beadcontained in a microwell.

According to an embodiment, there is provided a method for sequencing apolynucleotide strand, comprising: (a) disposing a plurality of templatenucleic acids into a plurality of reaction chambers disposed on a sensorarray, the sensor array comprising a plurality of sensors and eachreaction chamber being disposed on and in a sensing relationship with atleast one sensor configured to provide at least one output signalrepresenting a sequencing reaction by-product proximate thereto, andwherein each of the template nucleic acids is hybridized to a sequencingprimer and is bound to a polymerase; (b) introducing a known dNTP intothe reaction chambers where such known dNTP is selected from apredetermined ordering of dNTP flows; (c) detecting incorporation at a3′ end of the sequencing primer of one or more dNTPs by a sequencingreaction by-product if such one or more dNTPs are complementary tocorresponding nucleotides in the template nucleic acid; (d) washingunincorporated dNTPs from the reaction chambers; and (e) repeating steps(b) through (d) until the plurality of template nucleic acids have beensequenced.

According to an embodiment, there is provided a method of performingtemplate-based extension of a primer, comprising: (a) providing at leastone template having a primer and polymerase operably associated thereto;and (b) successively exposing the at least one template to nucleotidesflowed according to a flow ordering that is not a sequential andsuccessive four nucleotide ordering. The flow ordering may comprise“TACG TACG TAGC TGAC GTAC GTCA TGCA TCGA TCAG CTAG CTGA CGTA GCTA GCATCGAT CAGT CATG ACTG ACGT AGCT GACT GATC AGTC ATGC ATCG” (SEQ ID NO: 5),“TACT CAGT ATGC AGAC TGCG” (SEQ ID NO: 11), “TACG TACG TACT CAGC TAGCTAGT ATGC ATGC ATGC AGAC TGAC TGAC TGCG” (SEQ ID NO: 12), “TACG TACGTACT CAGC TAGT ATGC ATGC AGAC TGAC TGCG” (SEQ ID NO: 13), “TACG TACGTCTG AGCA TCGA TCGA TGTA CAGC” (SEQ ID NO: 7), “TACG TACG TACG TACG TACGTACA TACG CACG TGCG TATG” (SEQ ID NO: 6), or “TACG TACG TACG TACG TACGTACAT ACGCA CGTGC GTATG” (SEQ ID NO: 2), for example.

According to an embodiment, there is provided a method of determining asequence of a nucleic acid by template-based extension of a primer,comprising: (a) delivering a known nucleoside triphosphate precursor toa template-based primer extension reaction, the known nucleosidetriphosphate precursor being selected from a predetermined ordering ofdNTP flows; (b) detecting incorporation of the known nucleosidetriphosphate whenever its complement is present in the template adjacentto the primer; and (c) repeating steps (a) and (b) until the sequence ofthe nucleic acid has been determined, wherein the predetermined orderingof dNTP flows is adapted to improve phase synchronicity. Thepredetermined ordering of dNTP flows may be further adapted to reduceand/or at least partially corrects phasing effects associated withincomplete extension events. The predetermined ordering of dNTP flowsmay be further adapted to reduce and/or at least partially correctsphasing effects associated with carry forward events. The predeterminedordering of dNTP flows may be further adapted to reduce and/or at leastpartially corrects phasing effects associated with polymeraseefficiency.

According to an embodiment, there is provided a method for sequencing anucleic acid, comprising: (a) disposing a plurality of templates into aplurality of reaction chambers, each reaction chamber comprising atemplate having a sequencing primer hybridized thereto and a polymeraseoperably bound thereto; (b) introducing a known nucleoside triphosphateinto each reaction chamber selected from a predetermined ordering ofdNTP flows; (c) detecting sequential incorporation at the 3′ end of thesequencing primer of one or more nucleoside triphosphates if the knownnucleoside triphosphate is complementary to corresponding nucleotides inthe template nucleic acid; (d) washing unincorporated nucleosidetriphosphates from the reaction chamber; and (e) repeating steps (b)through (d) until the nucleic acid has been sequenced, wherein thepredetermined ordering of dNTP flows is defined by a plurality of flowssuch that nucleotides are not flowed in a series of consecutive repeatsof a predetermined four nucleotide ordering. The predetermined orderingmay comprise “TACT CAGT ATGC AGAC TGCG” (SEQ ID NO: 11), “TACG TACG TACTCAGC TAGC TAGT ATGC ATGC ATGC AGAC TGAC TGAC TGCG” (SEQ ID NO: 12),“TACG TACG TACT CAGC TAGT ATGC ATGC AGAC TGAC TGCG” (SEQ ID NO: 13),“TACG TACG TCTG AGCA TCGA TCGA TGTA CAGC” (SEQ ID NO: 7), “TACG TACGTACG TACG TACG TACA TACG CACG TGCG TATG” (SEQ ID NO: 6), or “TACG TACGTACG TACG TACG TACAT ACGCA CGTGC GTATG” (SEQ ID NO: 2), for example.

According to an embodiment, there is provided a method of sequencing apolynucleotide strand, comprising: providing the polynucleotide strandwith a primer annealed thereto and a polymerase operably bound to thepolynucleotide strand; and successively exposing the polynucleotidestrand to the flow of the four nucleotide species A, C, G, and Taccording to a predetermined ordering, wherein the predeterminedordering comprises a de Bruijn sequence ordering of the four nucleotidespecies A, C, G, and T with a de Bruijn subsequence length parameter oftwo or three and without any consecutive repeats of the same nucleotidespecies. The de Bruijn subsequence length parameter may be two. The deBruijn subsequence length parameter may be three. The predeterminedordering may consist of only the de Bruijn sequence ordering, or it mayinclude a portion that is a de Bruijn sequence ordering and a portionthat is not a de Bruijn sequence ordering. The method may furthercomprise detecting hydrogen ions released by incorporation of thenucleotides. The method may further comprise detecting inorganicpyrophosphate released by incorporation of the nucleotides. Theinorganic pyrophosphate may be detected by light emitted from an enzymecascade initiated by the inorganic pyrophosphate.

According to an embodiment, there is provided a method of sequencing apolynucleotide strand, comprising: providing the polynucleotide strandwith a primer annealed thereto and a polymerase operably bound to thepolynucleotide strand; and successively exposing the polynucleotidestrand to the flow of the four nucleotide species A, C, G, and Taccording to a predetermined ordering, wherein the predeterminedordering comprises a flow ordering that includes all possible distinctdimer pairs of the four nucleotide species. The possible distinct dimerpairs include AG, AC, AT, CA, CG, CT, GA, GC, GT, TA, TC, and TG.

According to an embodiment, there is provided a method of sequencing apolynucleotide strand, comprising: providing the polynucleotide strandwith a primer annealed thereto and a polymerase operably bound to thepolynucleotide strand; and successively exposing the polynucleotidestrand to the flow of the four nucleotide species A, C, G, and Taccording to a predetermined ordering, wherein the predeterminedordering comprises a flow of N followed immediately by a flow of X,where X and N represent different nucleotide species, and furthercomprises, immediately thereafter or elsewhere in the ordering, a flowof N followed immediately by a flow of Y, where Y represents anucleotide species different from both X and N. In an embodiment, theflows of N and Y may immediately follow the flows of N and X. In anotherembodiment, the flows of N and Y may not immediately follow the flows ofN and X.

According to an embodiment, there is provided a method of sequencing apolynucleotide strand, comprising: providing the polynucleotide strandwith a primer annealed thereto and a polymerase operably bound to thepolynucleotide strand; and successively exposing the polynucleotidestrand to the flow of the four nucleotide species A, C, G, and Taccording to a predetermined ordering, wherein the predeterminedordering comprises a flow of X followed immediately by a flow of N,where X and N represent different nucleotide species, and furthercomprises a flow of Y followed immediately by a flow of N, where Yrepresents a nucleotide species different from both X and N. In anembodiment, the flows of Y and N may immediately follow the flows of Xand N. In another embodiment, the flows of Y and N may not immediatelyfollow the flows of X and N.

According to an embodiment, there is provided a method of sequencing apolynucleotide strand, comprising: providing the polynucleotide strandwith a primer annealed thereto and a polymerase operably bound to thepolynucleotide strand; and successively exposing the polynucleotidestrand to the flow of four different nucleotide species according to apredetermined ordering, wherein the predetermined ordering comprises aflow ordering in which a first nucleotide species, a second nucleotidespecies, and a third nucleotide species are flowed at least twice beforea fourth nucleotide species is flowed. In an embodiment, the flowordering may be a first flow ordering and the predetermined ordering mayfurther comprise a second flow ordering in which the second nucleotidespecies, the third nucleotide species, and the fourth nucleotide speciesare flowed at least twice before the first nucleotide species is flowed.In an embodiment, the predetermined ordering may further comprise athird flow ordering in which the first nucleotide species, the thirdnucleotide species, and the fourth nucleotide species are flowed atleast twice before the second nucleotide species is flowed. In anembodiment, the predetermined ordering may further comprise a fourthflow ordering in which the first nucleotide species, the secondnucleotide species, and the fourth nucleotide species are flowed atleast twice before the third nucleotide species is flowed.

According to an embodiment, there is provided a method of sequencing apolynucleotide strand, comprising: providing the polynucleotide strandwith a primer annealed thereto and a polymerase operably bound to thepolynucleotide strand; and successively exposing the polynucleotidestrand to the flow of the four nucleotide species A, C, G, and Taccording to a predetermined ordering, wherein the predeterminedordering comprises a first set of flows and a second set of flows, thesecond set of flows being derived from a remapping of two or more of thenucleotide species in the first set of flows. In an embodiment, thesecond set of flows may be derived from a remapping of all four of thenucleotide species in the first set of flows. The remapping may involvea reassignment of each instance of the two or more nucleotide species inthe first set of flows.

According to an embodiment, there is provided a method of sequencing apolynucleotide strand, comprising: providing the polynucleotide strandwith a primer annealed thereto and a polymerase operably bound to thepolynucleotide strand; and successively exposing the polynucleotidestrand to the flow of the four nucleotide species A, C, G, and Taccording to a predetermined ordering, wherein the predeterminedordering comprises a flow ordering in which the same nucleotide speciesis contiguously flowed two or more times.

According to various embodiments, one or more features of any one ormore of the above-discussed teachings and/or embodiments may beperformed or implemented using appropriately configured and/orprogrammed hardware and/or software elements. Determining whether anembodiment is implemented using hardware and/or software elements may bebased on any number of factors, such as desired computational rate,power levels, heat tolerances, processing cycle budget, input datarates, output data rates, memory resources, data bus speeds, etc., andother design or performance constraints.

Examples of hardware elements may include processors, microprocessors,input(s) and/or output(s) (I/O) device(s) (or peripherals) that arecommunicatively coupled via a local interface circuit, circuit elements(e.g., transistors, resistors, capacitors, inductors, and so forth),integrated circuits, application specific integrated circuits (ASIC),programmable logic devices (PLD), digital signal processors (DSP), fieldprogrammable gate array (FPGA), logic gates, registers, semiconductordevice, chips, microchips, chip sets, and so forth. The local interfacemay include, for example, one or more buses or other wired or wirelessconnections, controllers, buffers (caches), drivers, repeaters andreceivers, etc., to allow appropriate communications between hardwarecomponents. A processor is a hardware device for executing software,particularly software stored in memory. The processor can be any custommade or commercially available processor, a central processing unit(CPU), an auxiliary processor among several processors associated withthe computer, a semiconductor based microprocessor (e.g., in the form ofa microchip or chip set), a macroprocessor, or generally any device forexecuting software instructions. A processor can also represent adistributed processing architecture. The I/O devices can include inputdevices, for example, a keyboard, a mouse, a scanner, a microphone, atouch screen, an interface for various medical devices and/or laboratoryinstruments, a bar code reader, a stylus, a laser reader, aradio-frequency device reader, etc. Furthermore, the I/O devices alsocan include output devices, for example, a printer, a bar code printer,a display, etc. Finally, the I/O devices further can include devicesthat communicate as both inputs and outputs, for example, amodulator/demodulator (modem; for accessing another device, system, ornetwork), a radio frequency (RF) or other transceiver, a telephonicinterface, a bridge, a router, etc.

Examples of software may include software components, programs,applications, computer programs, application programs, system programs,machine programs, operating system software, middleware, firmware,software modules, routines, subroutines, functions, methods, procedures,software interfaces, application program interfaces (API), instructionsets, computing code, computer code, code segments, computer codesegments, words, values, symbols, or any combination thereof. A softwarein memory may include one or more separate programs, which may includeordered listings of executable instructions for implementing logicalfunctions. The software in memory may include a system for identifyingdata streams in accordance with the present teachings and any suitablecustom made or commercially available operating system (O/S), which maycontrol the execution of other computer programs such as the system, andprovides scheduling, input-output control, file and data management,memory management, communication control, etc.

According to various embodiments, one or more features of any one ormore of the above-discussed teachings and/or embodiments may beperformed or implemented using appropriately configured and/orprogrammed non-transitory machine-readable medium or article that maystore an instruction or a set of instructions that, if executed by amachine, may cause the machine to perform a method and/or operations inaccordance with the embodiments. Such a machine may include, forexample, any suitable processing platform, computing platform, computingdevice, processing device, computing system, processing system,computer, processor, scientific or laboratory instrument, etc., and maybe implemented using any suitable combination of hardware and/orsoftware. The machine-readable medium or article may include, forexample, any suitable type of memory unit, memory device, memoryarticle, memory medium, storage device, storage article, storage mediumand/or storage unit, for example, memory, removable or non-removablemedia, erasable or non-erasable media, writeable or re-writeable media,digital or analog media, hard disk, floppy disk, read-only memorycompact disc (CD-ROM), recordable compact disc (CD-R), rewriteablecompact disc (CD-RW), optical disk, magnetic media, magneto-opticalmedia, removable memory cards or disks, various types of DigitalVersatile Disc (DVD), a tape, a cassette, etc., including any mediumsuitable for use in a computer. Memory can include any one or acombination of volatile memory elements (e.g., random access memory(RAM, such as DRAM, SRAM, SDRAM, etc.)) and nonvolatile memory elements(e.g., ROM, EPROM, EEROM, Flash memory, hard drive, tape, CDROM, etc.).Moreover, memory can incorporate electronic, magnetic, optical, and/orother types of storage media. Memory can have a distributed architecturewhere various components are situated remote from one another, but arestill accessed by the processor. The instructions may include anysuitable type of code, such as source code, compiled code, interpretedcode, executable code, static code, dynamic code, encrypted code, etc.,implemented using any suitable high-level, low-level, object-oriented,visual, compiled and/or interpreted programming language.

According to various embodiments, one or more features of any one ormore of the above-discussed teachings and/or embodiments may beperformed or implemented at least partly using a distributed, clustered,remote, or cloud computing resource.

According to various embodiments, one or more features of any one ormore of the above-discussed teachings and/or embodiments may beperformed or implemented using a source program, executable program(object code), script, or any other entity comprising a set ofinstructions to be performed. When a source program, the program can betranslated via a compiler, assembler, interpreter, etc., which may ormay not be included within the memory, so as to operate properly inconnection with the O/S. The instructions may be written using (a) anobject oriented programming language, which has classes of data andmethods, or (b) a procedural programming language, which has routines,subroutines, and/or functions, which may include, for example, C, C++,Pascal, Basic, Fortran, Cobol, Perl, Java, and Ada.

According to various embodiments, one or more of the above-discussedembodiments may include transmitting, displaying, storing, printing oroutputting to a user interface device, a computer readable storagemedium, a local computer system or a remote computer system, informationrelated to any information, signal, data, and/or intermediate or finalresults that may have been generated, accessed, or used by suchembodiments. Such transmitted, displayed, stored, printed or outputtedinformation can take the form of searchable and/or filterable lists ofruns and reports, pictures, tables, charts, graphs, spreadsheets,correlations, sequences, and combinations thereof, for example.

Various additional embodiments may be derived by repeating, adding, orsubstituting any generically or specifically described features and/orcomponents and/or substances and/or steps and/or operating conditionsset forth in one or more of the above-described embodiments. Further, itshould be understood that an order of steps or order for performingcertain actions is immaterial so long as the objective of the steps oraction remains achievable, unless specifically stated otherwise.Furthermore, two or more steps or actions can be conductedsimultaneously so long as the objective of the steps or action remainsachievable, unless specifically stated otherwise. Moreover, any one ormore feature, component, aspect, step, or other characteristic mentionedin one of the above-discussed embodiments may be considered to be apotential optional feature, component, aspect, step, or othercharacteristic of any other of the above-discussed embodiments so longas the objective of such any other of the above-discussed embodimentsremains achievable, unless specifically stated otherwise.

Although various embodiments of the present teachings may advantageouslybe used with sequencing-by-synthesis approaches, as described herein andin Rothberg et al., U.S. Pat. Publ. No. 2009/0026082; Anderson et al.,SENSORS AND ACTUATORS B CHEM., 129:79-86 (2008); Pourmand et al., PROC.NATl. ACAD. SCI., 103:6466-6470 (2006), which are all incorporated byreference herein in their entirety, for example, the present teachingsmay also be used with other approaches, such as variants ofsequencing-by-synthesis including methods where the nucleotides ornucleoside triphosphate precursors are modified to be reversibleterminators (sometimes referred to as cyclic reversible termination(CRT) methods) and methods where the nucleotides or nucleosidetriphosphate precursors are unmodified (sometimes referred to as cyclicsingle base delivery (CSD) methods), for example, or more generallymethods that comprise repeated steps of delivering (or extending inresponse to delivering) nucleotides (to the polymerase-primer-templatecomplex) and collecting signals (or detecting the incorporation eitherdirectly or indirectly).

Although various embodiments of the present teachings may advantageouslybe used in connection with pH-based sequence detection, as describedherein and in Rothberg et al., U.S. Pat. Appl. Publ. Nos. 2009/0127589and 2009/0026082 and Rothberg et al., U.K. Pat. Appl. Publ. No.GB2461127, which are all incorporated by reference herein in theirentirety, for example, the present teachings may also be used with otherdetection approaches, including the detection of pyrophosphate (PPi)released by the incorporation reaction (see, e.g., U.S. Pat. Nos.6,210,891; 6,258,568; and 6,828,100); various fluorescence-basedsequencing instrumentation (see, e.g., U.S. Pat. Nos. 7,211,390;7,244,559; and 7,264,929); some sequencing-by-synthesis techniques thatcan detect labels associated with the nucleotides, such as mass tags,fluorescent, and/or chemiluminescent labels (in which case aninactivation step may be included in the workflow (e.g., by chemicalcleavage or photobleaching) prior to the next cycle of synthesis anddetection); and more generally methods where an incorporation reactiongenerates or results in a product or constituent with a property capableof being monitored and used to detect the incorporation event,including, for example, changes in magnitude (e.g., heat) orconcentration (e.g., pyrophosphate and/or hydrogen ions), and signal(e.g., fluorescence, chemiluminescence, light generation), in whichcases the amount of the detected product or constituent may bemonotonically related to the number of incorporation events, forexample. Such other approaches may likewise benefit from the phasecorrection, signal enhancement, improved accuracy, and/or noisereduction features of the nucleotide flows approaches described herein.

Although the present description described in detail certainembodiments, other embodiments are also possible and within the scope ofthe present invention. For example, those skilled in the art mayappreciate from the present description that the present teachings maybe implemented in a variety of forms, and that the various embodimentsmay be implemented alone or in combination. Variations and modificationswill be apparent to those skilled in the art from consideration of thespecification and figures and practice of the teachings described in thespecification and figures, and the claims.

1-35. (canceled)
 36. A method for nucleic acid sequencing, comprising:disposing a plurality of template polynucleotide strands, sequencingprimers, and polymerases in a plurality of defined spaces of a sensorarray; exposing template polynucleotide strands to a series of flows ofnucleotide species, the series comprising a sequence of random flows;and obtaining, for each of the series of flows of nucleotide species, asignal indicative of how many nucleotide incorporations occurred forthat particular flow to determine a predicted sequence of nucleotidescorresponding to the template polynucleotide strands.
 37. The method ofclaim 36, wherein the series further comprises a de Bruijn sequence offour predetermined nucleotide species having a de Bruijn subsequencelength parameter of two or three and without any consecutive repeats ofthe same nucleotide species.
 38. The method of claim 36, wherein theseries further comprises a flow ordering that includes all possibledistinct dimer pairs of four nucleotide species.
 39. The method of claim36, wherein the series further comprises a flow of N followedimmediately by a flow of X, where X and N represent different nucleotidespecies, and further comprises, immediately thereafter or elsewhere inthe ordering, a flow of N followed immediately by a flow of Y, where Yrepresents a nucleotide species different from both X and N.
 40. Themethod of claim 36, wherein the series further comprises a flow of Xfollowed immediately by a flow of N, where X and N represent differentnucleotide species, and further comprises a flow of Y followedimmediately by a flow of N, where Y represents a nucleotide speciesdifferent from both X and N.
 41. The method of claim 36, wherein theseries further comprises a first flow ordering in which a firstnucleotide species, a second nucleotide species, and a third nucleotidespecies are flowed at least twice before a fourth nucleotide species isflowed.
 42. The method of claim 41, wherein the series further comprisesa second flow ordering in which the second nucleotide species, the thirdnucleotide species, and the fourth nucleotide species are flowed atleast twice before the first nucleotide species is flowed.
 43. Themethod of claim 42, wherein the series further comprises a third flowordering in which the first nucleotide species, the third nucleotidespecies, and the fourth nucleotide species are flowed at least twicebefore the second nucleotide species is flowed.
 44. The method of claim43, wherein the series further comprises a fourth flow ordering in whichthe first nucleotide species, the second nucleotide species, and thefourth nucleotide species are flowed at least twice before the thirdnucleotide species is flowed.
 45. The method of claim 36, wherein theseries further comprises a first set of flows and a second set of flows,the second set of flows being derived from a remapping of two or more offour nucleotide species flowed in the first set of flows.
 46. The methodof claim 36, wherein the series is selected based on an assessment ofdephasing merit and efficiency of extension calculated for a pluralityof candidate flow orderings using simulation sequencing data obtainedfor a plurality of random test sequences.
 47. The method of claim 36,wherein the series begins with a portion comprising repeats of a 4-flowpermutation of four different nucleotide species.
 48. A system fornucleic acid sequencing, comprising: a machine-readable memory; and aprocessor configured to execute machine-readable instructions, which,when executed by the processor, cause the system to perform stepsincluding: exposing template polynucleotide strands in a plurality ofdefined spaces of a sensor array to a series of flows of nucleotidespecies, the series comprising a sequence of random flows; andobtaining, for each of the series of flows of nucleotide species, asignal indicative of how many nucleotide incorporations occurred forthat particular flow to determine a predicted sequence of nucleotidescorresponding to the template polynucleotide strands.
 49. The system ofclaim 48, wherein the series further comprises a flow ordering thatincludes all possible distinct dimer pairs of four nucleotide species.50. The system of claim 48, wherein the series further comprises a flowof N followed immediately by a flow of X, where X and N representdifferent nucleotide species, and further comprises, immediatelythereafter or elsewhere in the ordering, a flow of N followedimmediately by a flow of Y, where Y represents a nucleotide speciesdifferent from both X and N.
 51. The system of claim 48, wherein theseries further comprises a flow of X followed immediately by a flow ofN, where X and N represent different nucleotide species, and furthercomprises a flow of Y followed immediately by a flow of N, where Yrepresents a nucleotide species different from both X and N.
 52. Thesystem of claim 48, wherein the series further comprises a first flowordering in which a first nucleotide species, a second nucleotidespecies, and a third nucleotide species are flowed at least twice beforea fourth nucleotide species is flowed.
 53. The system of claim 52,wherein the series further comprises a second flow ordering in which thesecond nucleotide species, the third nucleotide species, and the fourthnucleotide species are flowed at least twice before the first nucleotidespecies is flowed.
 54. The system of claim 53, wherein the seriesfurther comprises a third flow ordering in which the first nucleotidespecies, the third nucleotide species, and the fourth nucleotide speciesare flowed at least twice before the second nucleotide species isflowed.
 55. A non-transitory machine-readable storage medium comprisinginstructions which, when executed by a processor, cause the processor toperform a method for nucleic acid sequencing comprising: exposingtemplate polynucleotide strands, sequencing primers, and polymerases ina plurality of defined spaces of a sensor array to a series of flows ofnucleotide species, the series comprising a sequence of random flows;and obtaining, for each of the series of flows of nucleotide species, asignal indicative of how many nucleotide incorporations occurred forthat particular flow to determine a predicted sequence of nucleotidescorresponding to the template polynucleotide strands.